Solid State Phenomena Vols

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1 Solid State Phenomena Vols (009) pp 08- Online: (009) rans ech Publications, Switzerland doi:0.408/ Diagnostics Modeling of Vertical Rotor Vibration V. Barzdaitis, a, V. Žemaitis, b, R. Didžiokas, c, P. Mažeika, d aunas Universit of technolog, Donelaičio St.7, aunas, L-4444, Lithuania laipėda Universit, Bijūnų St. 7, laipėda, L-95, Lithuania a vtautas.barzdaitis@ktu.lt, b vtautas.zemaitis@ktu.lt, c rimantas.didziokas@ku.lt, d pranasmazeika@centras.lt ewords: vertical rotor, antifriction bearing, vibration, cavitation, modeling and simulation Abstract. his paper deals with condition monitoring and vibration diagnostics of vertical sulphuric acid pumps running in continuous long term operation mode. he task of eperimental testing and theoretical modeling to increase reliabilit and efficienc of vertical pumps through elimination of rotor lateral vibration. On the basis of eperimental testing results analsis the dnamic model was designed and simulated. he reason of high vibration of the pump rotor is the rotor technological bow and cavitation phenomenon that take place in the pump. Introduction he vertical rotors are rotating in antifriction bearings whose supports in tangential direction are not sufficientl stiff but radial stiffness predominates with variable snchronous dnamic stiffness [,]. Paper [] deals with the critical whirling speeds of shafts with two or three supports, or support and restraint, with an overhanging great disk taking into account both seeming and real groscopic effects. he resultant pulsation and the approimate oscillating bending moments and stresses, in the main critical, have been studied. he ecitation of these vibrations occurs when a moment originated b a periodic eccentricall thrust and/or a dnamic unbalanced moment, act over the disk. he most interesting cases in Engineering are the shaft sstems with helical aial impeller of propeller pumps, propeller of hdraulic aplan turbines and propeller of ships. H. anki and others [4] developed special eperimental model to realize the sub snchronous vibration of centrifugal compressor in laborator. he model is composed b ver light weight and large diameter impeller and ver slender shaft ton realize small sstem damping. he first test shows the tendenc for sub snchronous vibration. P. De Choudhur [5] has been presented detailed rotor-dnamic results along with comparison between the predicted and test results of three rotor-bearing sstems. he correlation of test results with the predicted lateral critical speeds obtained from stead state unbalance response analsis has been found to be good for different kinds of rotor bearing sstems. his paper deals with condition monitoring and faults diagnostic of vertical rotors in sulphuric acid pumps. he task of modeling, simulation and eperimental testing the identification of the causalit of dnamic forces and elimination of rotor lateral and aial vibration sources. Eperimental testing he two pumps of the same design were operating in snchronized mode recirculating sulphuric acid in continuous running mode taking acid from the tank. he level of the acid in the tank is stable and reaches.05 meters high measured from the bottom of the tank. he impeller is about 0, m from the bottom of the tank as shown in Fig.. he absolute vibration of the antifriction bearings housings were measured in (0-000 Hz) frequenc range b seismic transducer with vibration signal analzer Adash 400 (CZ). he casing vibration measurement transducer was attached at the antifriction bearing housing in radial and aial directions as shown in Fig., because the onl vibration data available will be casing absolute vibration of the rotor. All rights reserved. No part of contents of this paper ma be reproduced or transmitted in an form or b an means without the written permission of rans ech Publications, (ID: , Pennslvania State Universit, Universit Park, USA-/09/5,:0:55)

2 Solid State Phenomena Vols Antifriction bearing b) a) c) Fig.. he vertical sulphuric acid pump scheme (a, in inches), general scheme of two pumps unit (b) and bearing vibration measurement with accelerometer (c) (JSC Lifosa Courtes ) he pump #6 provides high vibration intensit level reaching radial and aial vibration velocit root mean square v rms 8mm / s values. he vibration signal is variable. he pump #60 has low vibration intensit level in comparison with pump #6 despite that both pumps have the same design and the same installation and operating conditions. he measured radial vibration velocit spectra of both pumps were shown in Fig. and the aial vibration velocit spectra in Fig. when the acid level in the tank is nominal H, 05m. he snchronous rotor response frequenc (X 5 Hz) radial vibration is dominant in the spectrum of both pumps #6. he super harmonic component (6X~ 50 Hz/0.86 mm/s) is dominant in pump #6, but low, Fig. b. he vibration spectrum indicates that pump #6 has unbalance or rotor is slightl bent. he aial vibration velocit spectra indicate that frequenc of super harmonic component (6X 48 Hz/.5 mm/s) is dominant in pump #6, Fig. b. he impeller has 6 vanes and the 6X harmonic is the vanes passing frequenc vibration. he vibration waves were observed on the oscilloscope in the time domain format and indicated the variable vibration in radial and aial directions. he Fig. and Fig. indicated that aial vibration measurement spectra are more informative than radial for diagnostics purposes, because the long rotor is attached to the less stiff tank plate in comparison with the radial stiffness of the project.

3 0 Mechatronic Sstems and Materials III a - pump #60, H=.05 m b pump #6, H=.05 m Fig.. Antifriction bearings housings radial vibration velocit spectra: a the pump #60 X 5 Hz v p_x 0,85 mm/s; b - the pump #6 X 5 Hz v p_x,6 mm/s; the 6X ~45 Hz v p_6x 0,86 mm/s; v rms.97-5,6 mm/s and variable a - pump #60, H=.05 m b - pump #6, H=.05 m Fig.. Antifriction bearings housings aial vibration velocit spectra: a the pump #60 X 5 Hz v pa_x 0,79 mm/s; b - the pump #6 X 5 Hz v pa_x 0.88 mm/s; the 6X ~48 Hz v pa_6x.5 mm/s; v arms mm/s is variable o identif the vibration sources OEM decided to increase acid level in the tank from.05 m up to.5 m and the pressure in the pipe is reduced. heoreticall, the flow rate will probabl rise, the horsepower requirement will probabl decreased and the pump will likel run smoother when the acid level rise up to.5 m. But vibration measurements results show that vane passing frequenc vibration increased on both pumps as shown in Fig. 4. he pumps starts vibrate more here is no N.P.S.H. (net positive suction head) available and the pump starts to cavitate. he reason of high vibration of the pump is the cavitations phenomenon. he collapsing of the acid bubbles in the surface of impeller vanes causes vibration as each vane encounter bubbles. he pump #60 does not have cavitation vibration (Fig. a, Fig. 4a). Acid flow recirculation disturbs flow balance through the impeller and consequentl high radial and aial forces are generated. his flow reversal and subsequent turbulent flow will cause increased vibration of both the rotor with impeller and the pump case.

4 Solid State Phenomena Vols a - pump #60, H,5 m b - pump #6, H,5 m Fig. 4. Antifriction bearings housings radial vibration velocit spectra: a the pump #60 X 5 Hz v p_x 0.57 mm/s, 6X ~50 Hz v p_6x 0.56 mm/s; b - the pump #6 X 5 Hz v p_x.0 mm/s, the 6X ~48 Hz v p_6x.5 mm/s, H,5m Pump #6 bearing housings vibration is still ver high and varies, when acid level increased from H.05m up to H.5 m. Rotor bearing housing absolute vibration velocit root mean square value v rms varies from.5 mm/s till 8. mm/s and eceeds safe operation values according API 670 norms described b OEM (v rms 5 m/s). Recirculation is the reversal of acid flow at the impeller tip. his is turbulent in nature and can cause cavitations like damage to the pump. When the impeller flow is disturbed in this manner it is possible that the flow balance through the impeller is disturbed and consequentl high radial and aial forces have been generated. his flow reversal and subsequent turbulent flow will cause increased vibration of both the rotor with impeller and the pump case. Vane passing frequenc vibrations are seen in bearing housing and pipe junction s absolute vibration velocit spectra. When a pump is running in recirculation mode the vanes impact with the acid flow that is traveling in a reversal direction. Cavitation is also likel to occur in flow regimes where recirculation occurs. Vane passing speed vibrations are caused hdraulicall b acid pressure waves. hat means that the forces from these pressure waves will be manifested on all internal surfaces of the pump and as such vibration ma be detected on the rotor, bearing housing as well as on the case or pipes junctions. o provide vibration displacement measurements of the shaft on the impeller impossible on such pumps design project. he operating condition of journal bearings running in the high temperature sulphuric acid media is complicated. Radial vibration displacement of the impeller is decisive for the safe operation of the two journal bearings and one antifriction bearing. he antifriction bearing housing absolute vibration velocit value is the main indicator for condition monitoring of the pump. he main difference between operation qualit of two pumps is that feature of the mechanical sstems to oppose and resist dnamic forces is different. he dnamic stiffness of two pumps is different. Dnamic stiffness consists of the long rotor longitudinal and lateral stiffness of the mechanical sstem elements complemented b the acid circumferential pressure wedge in the journal bearings, dnamic stiffness of mass and damping. Dnamic stiffness is a characteristic of a sstem, and it opposes an applied dnamic force to limit vibration response [6]. Rotor modeling and simulation A phsical model of a rotor sstem used for theoretical modeling is given in Fig. 7. he rotor is modeled specificall as designed dividing it into three parts proportional to the shaft lengths between the bearing supports. Each part is characterized b respective stiffness,, in lateral

5 Mechatronic Sstems and Materials III directions. Anisotrop of the supports is evaluated b two springs possessing respective stiffness H and V modeled in two perpendicular to each other directions X and Y. Fig.7. Phsical model of a rotor sstem Fig. 8. Vibration amplitude of rotor s impeller versus rotor free end stiffness For rotor modeling and simulation the mathematical model given in [] is adopted. When the masses M and M and damping are neglected, the rotor model has the familiar form for its two lateral displacements of the impeller: I I / l F cost I I / l F cos t (). where z i (t) = i (t) + j i (t), i =,,, j =, d / dt; z, z, z are rotor inboard, midspan and outboard lateral displacements (Fig. 7), M, M are shaft inboard and midspan modal masses, I and I are impeller transverse and polar moments of inertia,,, are shaft modal stiffness sections, H, V are stiffness of supporting springs, D is shaft damping coefficient, is rotative speed, l rotor length, V H / () are anisotropic stiffness and F, F,, combinations of midspan and outboard imbalanced masses, radii, shaft bows and their angular positions, respectivel. Model () represents the approimation of the first two lateral modes of the centrifuge rotor. Neglecting a groscopic term (I=0), but evaluating damping D, modified equation () has the following snchronous X solutions A cost, A sint where response amplitudes are: ()

6 Solid State Phenomena Vols F A, I / l D F A (4) I / l D Mass of the pump rotor M=00 kg; radius of the pump impeller R=0,65 m; length of the rotor l=4,08 m; mass of the unbalance m =0,0058 kg; radius of the unbalance r =0,0 m; rotative speed of the rotor Ω=54,98 /s; stiffness: = N/m; = N/m; = 0 6 N/m; stiffness of the springs are: V = H =0,5 0 6 N/m; damping coefficients are: D =D =6 0 N s/m. Mathematical model simulation results indicated that impeller radial vibration displacement amplitude A depends on the rotor stiffness as shown in Fig. 8. Summar. he cavitation phenomenon in the pump #6 is the main reason of high vibration level of the rotor bearing. Impeller vanes passing frequenc vibration is caused hdraulicall b acid pressure waves.. Aial measurements is more informative in comparison with radial measurements in case of vibration sources identification of long vertical pumps rotors.. Rotor s impeller radial vibration displacement amplitudes mainl depends on dnamic stiffness of the rotating sstem. he low frequenc periodic variation in vibration amplitude is generated as self-ecited vibration that is caused periodicall b the varing dnamic stiffness of the pump with sulphuric acid-fluid induced instabilit (internal energ transfer mechanism which delivers the energ in a periodic manner). References [] A. Musznska: Forward and Backward Precession of a Vertical Anisotropicall Supported Rotor. Journal of Sound and Vibration. 9() (996), p [] V. Barzdaitis, R. Jonušas, Z. Pocius, V. Žemaitis: Fleible vertical rotor modeling and dnamics. Mechanika. Nr. () (00), p [] Santamarina Pol, P.: Critical whirling speeds and oscillating stresses of shafts with overhanging disk sstems. Proceedings of the Ninth World Congress on the heor of Machines and Mechanisms IFoMM, Politechniko di Milano, Ital, August 9/September, Vol., 995. P [4] Hiroshi anki, azuhiko Adachi, Mitsutoshi Joutoku: Eperimental stud of destabilizing force from centrifugal compressor impeller. Proceedings of Fourth International Smposium on Stabilit Control of Rotating Machiner ISCORMA-4, Calgar, Alberta, Canada, 7- August 007. (Edited b Jerz. Sawicki and Agnes Musznska). P [5] P. De Choudhur: Rotor Dnamic Unbalance Response Correlation Stud. Proceedings of welfth World Congress in Mechanism and Machine Science IFoMM 007, June 7-, 007, Besancon France. Vol. 6, 007. P [6] A. Musznska: Rotordnamics. CRC press alor &Francis Group, Boca Raton, N.Y., London, Singapore, 005. p. 075.

7 Mechatronic Sstems and Materials III 0.408/ Diagnostics Modeling of Vertical Rotor Vibration 0.408/ DOI References [] A. Musznska: Forward and Backward Precession of a Vertical Anisotropicall Supported otor. Journal of Sound and Vibration. 9() (996), p doi:0.006/jsvi