THE DYNAMIC ANALYSIS OF CATALYTIC CONVERTER

Transcription

1 UNIVERSITY OF PITESTI FACULTY OF MECHANICS AND TECHNOLOGY SCIENTIFIC BULLETIN AUTOMOTIVE seres, year XX, no.24(1) THE DYNAMIC ANALYSIS OF CATALYTIC CONVERTER Ionel VIERU *, Vorel NICOLAE, Sebastan PÂRLAC Unversty of Ptest, Ptest, Romana Artcle hstory: Receved: ; Accepted: Abstract: The paper shows the modal analyss of analytc converter used n the engne exhaust system. For calculus s used a catalytc converter modeled by surfaces, usng CATIA V5 applcaton. On computes comparatvely the vbraton egenmodes for the catalytc converter housng, wth and wthout takng nto consderaton the ceramc monolth nfluence. The results obtaned by numercal calculus are compared wth expermental data acheved at the Unversty of Ptest. Keywords: catalytc converter, ceramc monolth, dynamc analyss, FEM INTRODUCTION Out of the engne nose sources ordered by loudness, the most mportant are the evacuaton of combuston gases and the fresh flud ntake. The effects of these two sources s attenuated wth slencers. The role of the exhaust s to evacuate the exhaust gases n the atmosphere n a form tolerable by human Startng wth the frst cars wth sgnfcant power, t was hghlghted the lghtng danger of the exhaust and the psychologcal dsorders caused by ts nose. Recent studes on the qualty of our vtal ambence draw attenton to the part of responsblty of the engnes for atmospherc polluton [1-4]. The converter desgned and presented n ths paper s used for a car equpped wth spark gnton engne, wth the cylnder capacty up to 2000 cm3. THE 3D CONVERTER MODEL The dgtal 3D model of the converter analyzed n ths paper was done usng the CATIA V5. The model s shown n Fgure 1. The housng unt of the converter s made of stanless steel of 1.5 mm thckness. Fgure 1. The 3D model of the catalytc converter. Generally, for the constructon of the housng t s used the ferrte sheet that has good mechancal strength and a good sound absorpton coeffcent, a good elongaton and a proper workablty. There are used the stanless materals because the reactons n the converter occur at hgh temperatures, wth * Correspondng author. Emal: onel.veru@upt.ro

2 water dsposal. In these condtons, the ordnary steel materals would damage (peel), and they may block or damage the ceramc monolth presented n Fgure 2. THE DYNAMIC CALCULUS Fgure 2. The ceramc monolth. CONSIDERATIONS REGARDING THE MODAL ANALYSIS The modal analyss conssts n determnaton of the dynamc characterstcs of structures and may nclude both analytcal and expermental processes. The descrpton of the dynamc characterstcs of the structure s done by determnng the vbraton egenmodes. Each mode of vbraton s assocated wth certan modal propertes, such as frequency, dampng, ampltude, mass, etc. These characterstcs of the structure may be determned at any pont thereof. The advantages of usng modal analyss n the study of a system consst n the evaluaton of the dynamc characterstc of the structure and the determnaton of ther frequences [5, 6, 7, 8]. MODAL ANALYSIS USING THE FINITE ELEMENT METHOD (FEM) Based on ts modal characterstcs, a structure s more or less senstve to vbratons. Ths senstvty to vbratons s characterzed by a number of extreme behavors to some frequences called vbraton egenmode. The numercal modal analyss determnes the modal characterstcs of a structure. The basc concept n the numercal modelng wth fnte s the concept of approxmatng the mesh. The approxmaton s an essental feature of the process of knowledge, representng one of the man forms of achevng t. It s mportant that the mesh s suffcently fne so that the modal deformatons to be represented correctly, beng necessary to have at least four s per wavelength. It may be carred out two types of modal analyss: - "free - free" (free frequency analyss) - when s not taken nto account the constrants (the boundary condtons); - the condtons mposed (the frequency analyss) - when the constrants are taken nto account. Durng the "free - free" modal analyss, the studed structure s consdered suspended and thus s not subject to any effort and any constrants. Ths type of analyss allows obtanng the pure characterstcs of a structure, wthout nfluences mposed by the constrants or the external envronment (forces, moments, etc.). A modal analyss can be carred out also wth the partcular boundary condtons; these constrants are met n most cases n the operatng condtons. Solvng the equaton of moton for the egenmodes matrx s wrtten as: M (1) u C u K u 0 where [M] s the mass matrx, [C] s the dampng matrx, [K] s the stffness matrx and u s the dsplacement vector [9, 10, 11, 12]. 45

3 A harmonc soluton adopted s: u sn t (2) where s the egenvector and s the own pulsaton. Substtutng the soluton nto the equaton of moton and smplfyng we get: 2 M 0 K (3) The non-trval egenmode soluton of the problem s reduced n terms of modal analyss to: 2 det K M 0 (4) The equaton (4) s reduced to : 2 0 K (5) M wth = 1, 2, 3,... 2 Each egenvalue and egenvector defne a free vbraton of the structure. The relatonshp between egenvalue, frequency f and own pulsaton s: f ; 2 MAKING THE CALCULUS MODEL (6) We choose a catalyst model generated by surfaces, whch s shown n fgure 3. For the calculaton of the vbraton egenmodes t has been used the module "Generatve Structural Analyss" of CATIA V5 for the case of hangng bodes, respectve the "free frequency analyss". The mesh was made of plateshaped s predomnantly quadrlateral, as shown n Fgure 4 [13]. There were analyzed to compare two ways of computng, namely: 1) there were calculated the vbraton egenmodes for the catalytc converter housng wthout takng nto account the nfluence of the ceramc monolth; 2) there were calculated the vbraton egenmodes for the catalytc converter housng by takng nto account the nfluence of the ceramc monolth. Fgure 3. The calculus model generated by surfaces. Fgure 4. The mesh created wthout the nfluence of the ceramc monolth mass. The number of s used n the two cases s shown n Table 1. The mass of the ceramc monolth (1.9 Kg) was located at a pont n the center of the converter housng usng the opton "mass dstrbuton" of the calculaton module as shown n Fgure 5. Table 2 presents the propertes of the materals used for calculaton. 46

4 Table 1. The number of s used for each model. Entty Wthout ceramc Wth ceramc Nodes Elements Fgure 5. The mesh created smulatng the nfluence of the ceramc monolth mass. Table 2. The propertes of the materals used for calculaton. Materal Steel Young's modulus 2e+011N_m2 Posson's rato Densty 7860kg_m3 Coeffcent of thermal expanson 1.17e-005_Kdeg Yeld strength 2.5e+008N_m2 In both cases there were analyzed the frst 30 vbraton modes. The results are presented n Table 3 for the frst 30 modes of vbraton n both cases (the rgd body modes are excluded from the lst). Mode number Wthout ceramc Wth ceramc Mode number Table 3. The calculated vbraton modes. Wthout ceramc Wth ceramc e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e+003 In both cases the frst sx modes of vbraton are equal to 0, whch was expected gven the case analyss used (free frequency analyss). Also, the egenmode frequences for the analyss takng nto account the nfluence of the mass of the ceramc monolth have lower values than the analyss wthout 47

5 the nfluence of the mass of the ceramc monolth. The vsual analyss of the egenmodes found that n the 30 vbraton modes calculated appear both torson and bendng global deformaton modes and local modes. The hgher frequency the mode shape becomes more complex. Fgure 6 and Fgure 7 llustrate the vbraton mode shape no. 21 (1909 Hz) for the second case. Fgure 6. The deformaton of the housng wth monolth for the vbraton mode no the upper face Fgure 7. The deformaton of the housng wth monolth for the vbraton mode no.21-the bottom face MEASURING THE NATURAL FREQUENCIES OF THE CATALYTIC CONVERTER THE MEASURING INSTRUMENTS USED The expermental measurements were done usng a measurng chan conssts of the followng s: accelerometer type PCB, 353B04 model, senstvty 1,011 mv/m/s 2 ; measurng amplfer; hammer for measurements. Software settngs: accelerometer, 1 Hz hgh-pass flter, FFT analyss up to 10,000 Hz; the FFT analyss was set to 3200 ponts of calculaton. These s are shown n Fgure 8. We used the ntegrated Soudbook system wth SAMURAI (SINUS Messtechnk GmbH) software specalzed n measurement and analyss of vbraton and nose. Ths software s dedcated to data acquston, sgnal analyss and control of varous devces and external equpment. The hammer used to strke the pece n order to acheve the vbraton s specfcally for measurement of vbratons and ncorporated theren a power transducer that s used n some measurements. Fgure 8. The devce used for measurements. 48

6 Multple measurements were made manly n two cases, namely: wth the converter suspended (Fgure 9) and wth the converter mounted n the overall exhaust assembly (Fgure 10). Fgure 9. The converter suspended. Fgure 10. The converter mounted n the overall exhaust assembly. THE EXPERIMENTAL RESULTS The determnatons were performed by several experments n whch the accelerometer was mounted n varous postons on the catalyst, and t was excted n dfferent drectons. Fgure 11 shows the results obtaned wth the suspended converter, the accelerometer mounted centrally dsposed and the transverse exctaton, and Fgure 12 shows the results when the accelerometer s centrally dsposed and the exctaton s longtudnal. Fgure 11. The results wth the accelerometer centrally dsposed and transverse exctaton. Fgure 12. The results wth the accelerometer centrally dsposed and longtudnal exctaton. It could be observed that n both cases the maxmum values of vbraton ampltude s around 2000 Hz, so close to the vbraton mode no. 21. For the values greater than 2000 Hz, the analyzed sgnal ampltude decreases. The results of the expermental measurements for the exhaust assembly are shown n Fgure 13. Fgure 13. The results of the expermental measurements for the exhaust assembly. 49

7 CONCLUSIONS For the measurements done wth the converter mounted n the exhaust assembly, t was observed that the sgnal keeps generally the same shape but the maxmum values of the ampltudes are obtaned for frequences below 2000 Hz. Once determned, the egenfrequences can be used for: - frequency analyss and transent analyss; - expermental analyss; - optmze the dynamc behavor of structures. In the modal analyss, the dynamc response of the structure s the sum of the ndvdual egenmodes of vbraton. By determnng the characterstcs of the vbraton modes usng expermental and / or analytcal means, t s possble to determne what undesrable responses (nose, vbraton, great efforts) are created and to formulate the correctve acton. REFERENCES [1] D.L. Davs, G. E. Onsh, Catalytc Converter Development Problems, SAE [2] Heck, R.M. and R.J. Farrauto, "Automoble exhaust catalysts," Appl. Catalyss. A: Gen., 221, (2001). [3]Krchner T. and Egenberger G., "On the dynamc behavour of automotve catalysts," 1997, Catalyss Today Vol.38, pp [4] Rajadura, S. and Tagomor, M., "Catalytc Converter Desgn, Development and Manufacturng," SAE Techncal Paper , [5] Ewns, D.J., Modal Testng: Theory, Practce and Applcaton. Second edton (2000). ISBN [6] N. Karuppah, C. Sujatha, V. Ramamurt, Modal and Vbraton / Stress Analyss of a Passenger Vehcle by FEM, SAE [7] Storck, H., Sumal, H., and Pu, Y., "Expermental Modal Analyss of Automotve Exhaust Structures," SAE Techncal Paper , [8] A.K.M. Mohuddn and Muhammad Nurhafez,2007., Expermental analyss and comparson of performance characterstcs of catalytc converters ncludng smulaton, Internatonal Journal of Mechancal and Materals Engneerng (IJMME), Vol. 2, No. 1, 1-7. [9] Prest, M., Pace, L., et al., 2002, A Computatonal and Expermental Analyss for Optmzaton of Cell Shape n Hgh Performance of Catalytc Converters, SAE Paper [10] Cho, J., Cho, Y., Na, J., Lee, J. et al., "The Total Fnte Element Analyss System for the Desgn of an Automotve Catalytc Converter," SAE Techncal Paper [11]Koltsaks, G. C., Konstantnds, P. A. and Stamatelos, A. M., 1997, "Development and Applcaton Range of Mathematcal Models for 3-way Catalytc Converters," Appled Catalyss B: Envronmental, Vol.12, pp.161~191 [12]Koltsaks, G. C. and Stamatelos, A. M., "Dynamc Behavour Issues n Three-Way Catalyst Modelng," 1999, AIChE J. Vol.45, No.3, pp.603~614 [13] *** CATIA V5 Documentaton. 50