Transactions on Modelling and Simulation vol 10, 1995 WIT Press, ISSN X

Transcription

1 Fatigue failure of suspension tubes in a catalytic reformer furnace R.C. Batista, M.S. Pfeil, N. Roitman COPPE - Federal University of Rio de Janeiro, C. Postal Abstract The consolidation of catalytic material inside the suspension tubes of a reformer furnace is usually achieved through vibration procedures that may cause damages to the welded tubular joints. This paper reports on the main results obtained from an interactive numerical-experimental dynamic approach to this vibration problem, which had a twofold purpose: (i) to calibrate a FEM model to perform a fatigue analysis; (ii) to conceive an alternative procedure which precluded the precocious fatigue cracks in the welded joints. 1 Introduction In a hydrogen production plant the consolidation of the catalytic material inside the vertical tubes of a reformer furnace can be done by applying lateral forced vibration through a pneumatic device mounted at the top of each of these suspended tubes, as illustrated in Fig. la-c. This procedure, sometimes adopted to speed up the consolidation process, can cause however considerable fatigue damages and early cracks in the welded joints (see detail in Fig.lc) of the nonstructural steel tubes, leading to the disruption of the production plant [1]. This paper reports on the various stages, and presents the most relevant results, of an interactive numerical-experimental dynamic analysis which was performed to investigate and solve the problem. The mechanical behaviour and the forcing load were first identified by experimental measurements and the acquired data was used to calibrate a FEM model in terms of time and frequency responses. This calibrated numerical model then allowed for calculating fatigue damages and for conceiving an alternative and more efficient

2 708 Computational Methods and Experimental Measurements dynamic consolidation procedure which precluded the precocious occurrence of fatigue cracks. Description of the structure and FEM model As shown in Fig. 1 the main vertical tubes are suspended from pretensioned helical springs to allow for thermal strains induced by high temperatures in the furnace. Flexible pigtails connect the main vertical tubes to the headers, the top one kept "floating" by counterweights. These flexible pigtails allow for variations in length of both pretensioned springs and heated vertical tubes. Because of the described mechanical characteristics the interaction effects between the tubes due to pretensioning, thermal straining or forced vibrations can be altogether neglected and the FEM modeling very much simplified. Only one vertical tube plus its top and bottom pigtails were discretized by using ordinary space frame elements and elastic connections plus inertial boundary conditions to represent the prestressed structure and the links between pigtails and headers. 2 Experimental analysis Experimental dynamic responses of the suspension tubes were obtained for two distinct conditions: free vibrations under impacts produced by a rubber-hammer. forced vibrations caused by the pneumatic shaker. Eleven micro-accelerometers (Kyowa, Ig), eight of which located as shown in Fig. 2(a) were used to record the dynamic responses in terms of axial and transversal accelerations of various points along the main tube. The acceleration signals were acquired and processed by using the data A & P systems indicated schematically in Fig. 2(b). In each free vibration test the instrumented tube was excited by a series of impacts in distinct points and directions in order to identify through multipoint time histories the largest possible number of vibration modes. Their associated natural frequencies were obtained by applying the Fast Fourier Transform algorithm to the recorded acceleration signals, resulting in frequency spectra. Damping factors for the lowest vibration modes could be easily evaluated through the logarithm decrement technique. Rigid body motion related to pendular surge of the main tube was estimated as 80% of critical damping. In each forced vibration test the air pressure in the pneumatic shaker was slowly varied within the range atm. The magnitude of the excitation force versus time was calculated approximately by using the shaker's mass as the multiplier of the digitalized signal from micro-accelerometer AGIO (see Fig. 2a) attached to the shaker itself. For the pressure of 3.0 atm the excitation force time history is shown in Fig.3a, and as shown by its spectrum (Fig.3b) it is

3 Computational Methods and Experimental Measurements 709 dominated by a frequency very close to 170 Hz, along with low frequencies around 0.4 Hz. 3 Numerical analysis Theoretical dynamic analysis were performed for: free vibrations under initial stresses caused by pretensioned spring. forced vibration caused by pneumatic shaker at a working pressure of 3.0 atm. The simplified FEM model had its mesh increasingly refined to match the experimental data for natural frequencies and associated vibration modes. Many modes with frequencies in the range Hz were found from the free vibration analysis. Among these, the following dominant modes could be readily identified (Fig. 4): rigid body motions of the main vertical tube (Fig. 4.a) with frequencies in the range 0.5 to 3.0 Hz, due to little restraint to lateral movements offered by the helical spring. bending predominant modes of the main tube with various frequencies in the range 5.0 Hz Hz (Fig. 4b) A mass proportional damped modal analysis in the time domain was used to obtain the dynamic responses under forced vibrations. The excitation force was mathematically described by a Fourier series and the modal analysis was performed by superimposing 31 natural vibration modes, considered as the most relevant to the analysis as far as the range of dominant force frequencies are concerned. Figure 5 shows the forced vibration response in terms of the displacement in the X direction at the joint between the conical and cylindrical sections, where cracks occurred. It can be observed in this figure that the amplitude of response reaches minimum and maximum values close to -2.0 mm and +1.5 mm respectively and that the dynamic response is clearly dominated by a low frequency mode (0.5 Hz) coupled to a high frequency mode (170 Hz) whose amplitude was found to be around ± 0.05 mm. 4 Correlation between numerical and experimental results Some few results selected among the most representatives [1] are brought herein to demonstrate the good correlation between numerical and experimental results that was achieved by simply increasing the mesh refinement and by representing the most approximately as possible the actual forcing function and all the geometrical and physical properties of both main structural model and its links to substructures, the latter simulated through well defined geometric and inertial boundary conditions. Table 1 presents the correlation for some bending vibration frequencies and gives their corresponding mode shapes in terms of the number of half-waves along the height of the main tube. Typical numerical and experimental responses

4 710 Computational Methods and Experimental Measurements in terms of acceleration are superimposed in Fig.6 to demonstrate together with Table 1 that the numerical results obtained with the calibrated FEM model correlate favourably, both qualitative and quantitatively with their experimental counterparts. 5 Fatigue analysis Table 1 - Correlation between natural frequencies (Hz) Experimental (Hz ± 8 Hz) Numerical Mode-shape ACT ACS AC (Hz) (half-waves) = measurement error, ranging from 0.04 to 0.4 Hz The calibrated model was used to estimate fatigue damages produced by the pneumatic shaker and thereby elucidate the main causes of the detected cracks. The total elapsed time to complete the consolidation process of catalytic material inside each vertical tube was estimated to be t^ = 10 4 sec., corresponding to the consolidation of 100 kg of material in 20 batches of 5 kg Fatigue life was estimated by using the power-spectral-density function (PSDF) of the stress response amplitude S(t) form(=31) vibration modes Sg(f) = I S(f) Sm,Sm (1) where f is the variable driving frequency and the summation on the right-hand side of Equation. 1 is carried out on the PSDF for the stress modal response Sm(f) In the present analysis Sg(fj was obtained directly by applying the Fast Fourier Transform algorithm (FFT) onto the stress time history yielded by the modal analysis in the time domain. Stresses variations at the weld toe of the joint between conical and cylindrical sections were multiplied by a stress concentration factor SCF=2.5 that corresponds to the minimum design value recommended for welded tubular joints [2]. The forcing function is actually narrow-banded and cumulative fatigue damage was calculated by assuming a Rayleigh probability density function, where a,, is the rms stress response

5 Computational Methods and Experimental Measurements 711 Total fatigue damage in the time interval of the consolidation process was then calculated with Dy = Z Dy H; Dy = % [(p(s)as) / N(S) (3) %b where Dy is the fatigue damage in the elapsed time interval (ty%500 sec.) to consolidate each batch of material, n*,<20 is the number of batches, N(S) is the number of cycles for failure at stress range S, obtained for the appropriate S-N curve [3,4], and AS is the stress increment used in the summation procedure. The estimated fatigue damage led to a fatigue life T = 3.7 x 10* sec. which has the same order of magnitude of the estimated total elapsed time to complete the consolidation process (t^w sec.). Then it is highly expected that fatigue cracks at the considered welded joint can be initiated very early, before consolidation completion. 6 Problem solution By using the experimentally calibrated FEM model an alternative solution to this problem could only be found by applying low frequency axial vibration forces to the tube; these can be envisaged by short duration axial impacts of magnitude equal to IkN produced by a pair of pneumatic hammers (as illustrated in Fig. Id) in alternate operation in a frequency equal to 1/2 Hz. The system response for this loading resulted in small amplitudes of the bending modes and, consequently, in a much higher fatigue life expectancy. 7 Concluding remarks The most relevant aspects of an interactive theoretical-experimental-numerical approach to a practical engineering problem are emphasized. Simple but consistent numerical modeling and experimental analysis techniques are applied orderly and interactively to analyze a typical structural vibration problem and to seek a practical solution to preclude premature initiation of fatigue cracks in the welded joints of steel tubes in a reformer furnace, caused by the adopted dynamic procedure to consolidate the catalytic material inside these tubes. References 1. Batista, R. C. Vibration Analysis of the Suspension Tubes in the Furnace H-6201, Reduc Petrobras, Contract Report COPPETEC ET-15390, Rio de Janeiro, Sept

6 712 Computational Methods and Experimental Measurements 2. Det Norske Veritas, DNV. Rules for Fatigue Design - Steel Strucutres, Gurney, T. R, Fatigue Design Rules for Welded Steel Joints, The Welding Institute Research Bulletin, May New Fatigue Design Guidance for Steel Welded Joints, (Issue 3), in Offshore Installations: Guidance on Design and Construction, Department of Energy, U.K., May TOP \ i ur ncfi\ui COUNTERWEIGHTS -^f, ROD RO ' 1 0) - * ' * L SPRING ^_SUBflUP \ FLANGE s SEE DETAIL > ; DETAIL /\ HOT-BASE (PIPE-SHAPED) 14 MAIN TUBES 1 BOTTOM PIGTAILS \ FURNACE \ 4 ' i^ )gj h =-- \ ROTTOM HFADFR (a) SIDE VIEW (b) FRONT VIEW _J 0 U3 ' ^x<.1 fl ' FRACTURED! ' i SECTION ' g bo 737 mr PNEUMA Tl\C \ SHAKER (c) FRACTURE CAUSEL~) BY APPLIED VIBRATION 1 BEAM j \x F1 F2 F2 NEUMA TIC HAMMERS BOTTOM PIGTAIL ^ t (d) AL TERNA TIVE VIBRA TION PROCEDURE 2 sec Figure 7-Suspension tubes system (all dimensions in mm) and vibration procedures

7 Computational Methods and Experimental Measurements 713 'ACll 2L3 3BC AC4 Figures 2 % ACS' PNEUMATIC,- % = SHAKER AC7m % AC 9m TAPE RECORDER q < 3 (a; fa) Instrumentation plan (b) Data A & P systems DATA ACQUISITION SYSTEM 11 ACCELEROMETERS 12 CHANELS AMPLIFIER AND FILTER E E : TAPE RECORDER DATA PROCESSING SYSTEM A CCELERA TION x TIME i A/U \ JLL^JL W DISPLACEMENT x TIME DOUBLE INTEGRA TOR PC natural frequencies 1 luw SPECTRUM onr^-rn,,.. ANAL a.,.,.,mrn YSER -^ '.P ==^^ 1 PLOTER M TIME (sec) Figures 3 - (a) Force time history (b) Force power spectrum (b) FREQUENCY (Hz) (a) f =0.5 Hz (b) f=40.6 Hz i (c) f= Hz Figure 4 - Vibration mode shapes

8 714 Computational Methods and Experimental Measurements - - time (sec) 4 Figure 5 - Lateral displacement at the pigtail - top header joint for forced vibration (3 atm) -90 numerical experimental o time (sec) 0.10 Figure 6 - Experimental and numerical acceleration time responses at the top pigtail- top header joint