A modal approach for vibration analysis and condition monitoring of a centrifugal pump Abstract Ramana Podugu Research scholar, Mechanical Engineering Department. JNTU, Hyderabad,Andhra Pradesh,India. ramana.p755@gmail.com J.Suresh Kumar Associate Professor, Associate Professor, Mechanical Engineering Department. JNTU, Hyderabad,Andhra Pradesh,India. B.V.Ramana murthy Principal, Visakha Institute of Engineering & Technology Visakhapatnam,Andhra pradesh. N.Syam Kumar Scholar,AU,Visakhapatnam,AP. The modal analysis of the centrifugal pump and its assembly is performed using FEM technology. The mathematical model and FEA model are built for the original centrifugal casing and simulation is made to find the pump natural frequencies. The first ten natural frequencies were compared to pump operating speed and their multiples up to pump vane passing frequency as per HIS (Hydraulic Institute Standards -9.6.4-2000) guidelines. In the original design, the first natural frequency in vertical direction of the pump is found to be the cause for resonance at the first multiple speed of the pump. The first natural frequency of the original model was found to be 63.25 Hz which is very close to 62.5 Hz of the pump operating speed by a margin of 1.2%. As per HIS clause 9.6.4.4, the first natural frequency should be 10% above or below the pump operating speed. Finally, the model was modified by stiffening the pump pedestals and again FEA analysis was carried out to find the natural frequencies. As a result of modification in design, the first natural frequency was increased to 74.31Hz which is above 10% the pump operating speed i.e., 62.5 Hz. Hence, the results of the modified design are satisfied with HIS clause. The results also show that the higher the stiffness of the pump, higher the natural frequency is. Keywords: API, Centrifugal pump, FEM, modal analysis, vibration, HIS. 1. Introduction Centrifugal pump consist of a stationary pump casing and an impeller. The main function of pump casing is to guide the liquid from the suction nozzle to the centre of the impeller. Impeller impart a radial and rotary motion to the liquid, which results in increase in both the pressure and the kinetic energy and forcing it to the volute. The purpose of the volute is to collect the discharged liquid from the periphery of the impeller at high velocity and gradually cause a reduction in fluid velocity by increasing the flow area. This converts the velocity head to static head. The fluid is then discharged from the pump through the discharge nozzle Vibration problems are most commonly associated with centrifugal pumps. The sources of vibration in centrifugal pumps can be categorized into three types such as Mechanical causes, Hydraulic causes & Peripheral causes. Level of imbalance and the level of misalignment are the important reasons of mechanical and hydraulic causes. The peripheral causes of vibration include Harmonic vibration from nearby equipment or drivers, ISSN : 0975-5462 Vol. 3 No. 8 August 2011 6335
operating the pump at critical speed. Problems with any of these issues will show up as symptoms, which include higher than normal vibration at certain key frequencies. The reliability and performance of any centrifugal pump system can be directly affected by its dynamic characteristics. Yesh P. Singh [1], who worked on A finite elements approach for analysis and design of pumps, showed that changes in system dynamics as the addition of vibration control elements. Jyoti K. Sinha [2], and A. Rama Rao, conducted Modal analysis on the complete assembly of pumps, piping layout and identified resonance as the root cause for pump failure. Bernd durrer [3] explained noise sources in centrifugal pumps and possible remedies and their effect on noise reduction. Cornelius [4], Scheffer, conducted an experiment on Pump Condition Monitoring through Vibration Analysis It is well-known that vibration analysis is a powerful tool for the condition monitoring of machinery. Ravindra Birajdar [5],addressed general causes of noise and vibrations, its diagnosis and remedies in centrifugal pumps. Giacomo Marenco [6], has experimentally investigated the effect bearing housing design will influence the dynamic characteristics of the system. In this paper an attempt is made on effect of the base plate stiffness in improving the dynamic characteristics of the pump assembly. To ensure the safety of the pump and associated plant components, the vibration and noise must be kept within certain limits. Typical reasons for pump failures can be diagnosed well in advance by applying the right kind of vibration testing, analysis, and evaluation criteria during pump monitoring or troubleshooting. This paper describes the modal analysis carried out for the centrifugal pump assembly. It explains how a reduced separation margin between running speed and the natural frequencies of the machine is the main cause for high vibrations in machines during operation. To study this issue, a finite element model of the pump was setup and calibrated with experimental data. This paper describes how the assembly of the centrifugal pump can be improved dynamically by adding the stiffeners at appropriate locations. 2. Description of the pump A CAD representation of the entire centrifugal pump and its assembly can be seen in Fig. 1. A pump consists of the shaft which is supported by two bearings. One end of the shaft is connected to the coupling and other end of the shaft is connected to the impeller which is in overhung position. It also holds other rotating components such as mechanical seal throttle and sleeve bush etc. Bearing housing consists of bearings through which shaft is fitted. The entire pump assembly is mounted on the base plate which in turn is anchored to the foundation at the foundation holes. The volute casing comes under category of a horizontal centrifugal pump.it is single volute centrifugal pump casing with an impeller consisting of four vanes.. Casing is a single piece casting with no welded joint. At its best efficiency point the pump runs at 3600 RPM with flow rate of 45 m3/hr and head of 50m. The outside diameter of the impeller is 309.57 mm and width of the impeller including shroud is 39 mm.the volute is built by lofting its cross-sectional area at different plans on the base circle. The cross sectional area of the volute passage is minimum at the tongue region and maximum at the discharge end. ISSN : 0975-5462 Vol. 3 No. 8 August 2011 6336
Fig 1.Centrifugal pump casing assembly. 3. FEA modeling of modal analysis 1.1. Finite Element analysis methods: Equation of Motion of the forced damped system is shown in equation (1).X (t) interacting with a square mass matrix, M, stiffness matrix, K, damping matrix, C, and externally applied force vector, F (t). The corresponding SHM, or free vibration mode (C = 0, F = 0) for a finite element system is The SHM assumption generalizes to X (t) = u sin (ωt) where ω is the frequency of the harmonic motion. This leads to the general matrix Eigen value problem Equation (3) represents the Eigen value problem associated with matrices [m] and [k].this can be expressed in the form 2 This equation is called as the characteristic equation, ω is known as the Eigen value and ω is called the natural frequency of the system. A n-order algebraic expression can be obtained from eq. (4) is 2 The solution of the above equation gives n values of ω.it can be shown that all the n roots are real and 2 2 2 positive when the matrices[k] and [m] are symmetric and positive definite. If ω ω 2 n denote the n 1,,..., ω ISSN : 0975-5462 Vol. 3 No. 8 August 2011 6337
roots in ascending order of magnitude, their positive square roots gives the n natural frequencies of the system ω1 ω2... ωn..the lowest value( ω 1 ) is called the fundamental or first natural frequency 4. Finite element analysis FEA modal analysis of the pump was carried out for the quick identification of natural frequencies for the assembly. Later, Harmonic analysis was performed to note the high amplitude (displacement or acceleration) in the span of zero to 500 Hz. The pump was analyzed without considering the piping connections and the motor coupling because their influence in this analysis is negligible. Furthermore, they are the conditions mandated by API 610 for bearing housing resonance testing (paragraph 7.3.4.6) [9]. The following steps are used to perform the FEA analysis. 4.1 Model: The geometrical dimensions of the casing, casing cover, shaft, bearing housing and base plate are shown in fig (2).The geometrical parameters of the pump casing and casing cover are listed in table 1 Table 1: Geometrical dimensions Casing body dimensions Casing cover dimensions Outside dimater,dc(mm) 469.5 Outside diameter,dc 425.45 Volute thickness,tw(mm) 20.65 Thickness 52.4 Fig 2.Cross sectional view of the centrifugal pump casing and with base plate 4.2 Material Properties: A216 WCB material is used for the casing, cover plate and bearing housing. Material A479 type 410 is used for pump shaft A217 CA15 type material is used for Impeller. Structural steel grade 36 is used for the base plate material. Material data which is used for all components are listed in Table (2). ISSN : 0975-5462 Vol. 3 No. 8 August 2011 6338
Table 2, Material properties A216 WCB material for casing and casing cover and Bearing housing Density Young's modulus Poison ratio Yield stress Ultimate stress Kg/m3 Mpa Mpa Mpa 8000 202710 0.3 248.21 482.63 A479 Type 410 material for Pump shaft Density Young's modulus Poison ratio Yield stress Ultimate stress Kg/m3 Mpa Mpa Mpa 7695 201330 0.3 275.79 482.63 A217 CA15 material for Impeller Density Young's modulus Poison ratio Yield stress Ultimate stress Kg/m3 Mpa Mpa Mpa 7695 201330 0.3 448.16 620.53 A36 Carbon steel material for Base plate Density Young's modulus Poison ratio Yield stress Ultimate stress Kg/m3 Mpa Mpa Mpa 7861.1 202710 0.3 250.28 399.9 4.3 Meshing and Boundary conditions: Meshing modal of the pump volute casing is shown in fig 4. In this FE model a higher order element, solid 186 is used for entire model. This element is a 20-node tetrahedral element [9]. The information of the solid 186 element is shown in Fig 3. The total no of nodes and elements are 271887 and 168571 respectively. Elements were sufficiently refined until results of the analysis became mesh independent. Non-critical sections such as bolt holes were removed. Eight foundation holes are fixed in all directions (i.e.x, y, and z) as shown in fig (5). ISSN : 0975-5462 Vol. 3 No. 8 August 2011 6339
Fig 3: Solid 186 structural solid elements Fig 4: Mesh Model Fig 5: Boundary conditions 5. Results and discussions In this section the first ten natural frequencies are calculated from finite element analysis and listed in the Table 3 and first two mode shapes are graphically shown in fig 6. It was observed that the first natural frequency 63.252 Hz is very close to operating speed 62.5 Hz and the separation margin differ by 1.2%. This less separation margin causes high vibration during operation. Further harmonic analysis is also performed to find the maximum amplitude at the frequency of 62.5 Hz as shown in fig 7 and fig 8. ISSN : 0975-5462 Vol. 3 No. 8 August 2011 6340
Table 3: First ten natural frequencies Mode Natural frequency (Hz) (Operating speed) 1st speed (Hz) Margin in % 1 63.25 62.5 1.20 2 83.89 62.5 34.23 3 106.83 62.5 70.93 4 129.83 62.5 107.73 5 156.72 62.5 150.75 6 166.32 62.5 166.11 7 182.50 62.5 192.00 8 192.70 62.5 208.32 9 225.54 62.5 260.86 10 245.73 62.5 293.17 Fig 6 Mode shapes for the original design Fig 7 shows both the position and direction of the applied force for the modal analysis of the centrifugal pump.force is applied at the drive end location because the test results showed maximum highest vibration at the same location. The maximum amplitude plot is shown in fig 8. Fig 7. Force and measurement location at the bearing location. Fig 8. Amplitude response in vertical direction ISSN : 0975-5462 Vol. 3 No. 8 August 2011 6341
6. Experimental results The following figure shows the experimental test results of the pump assembly. The data were recorded using a spectrum analyzer. Vibration measurements are taken at the inboard and outboard bearings of a pump in axial, horizontal, and vertical directions by bump test. The frequency range in vertical direction is considered for the analysis spanned 0 to 500 Hz. The higher peaks are noted in the above range during performance tests. From the frequency response and phase diagram (2nd row and 2nd column of fig.9), the peak amplitude is shown at 3750 RPM (62.5 Hz). This is due to the resonance occurred at the first natural frequency which was proven from FEA results as explained under section 4. Fig 7: Experimental r Fig 9. Experimental test results To avoid the resonance at the operating speed, the first natural frequency needs to be increased. The total stiffness of the system depends on casing geometry and base plate structural design. Since the casing geometry is related to the hydraulic profile, it cannot be altered. The increase in base plate stiffness can be verified by many ways either by adding a number of cross members underneath the slant plate, increasing the size of the long run channel or by altering the pedestal design. There are some other factors that need to be considered are cost and manufacturability. After analyzing the structural behavior of the system, it has been observed that the effective increase in stiffness can be achieved by pedestal redesigning. 7. Modified design and FEA analysis: From the mode shape diagrams shown in fig. 6, the first mode represents the bending mode in vertical direction. It is clear that the pedestal stiffness needs to be increased on x-y plane. This is achieved by adding two stiffener plates on either side of each pedestal as shown in the fig.10 ISSN : 0975-5462 Vol. 3 No. 8 August 2011 6342
Fig 10: Stiffener plates are attached to pump pedestals. The FEA steps from 3.1 through 3.5 were repeated for the modified model to calculate the first ten natural frequencies, which are listed in table 4.First two mode shapes are shown in fig 11. Table 4: the natural frequencies with modified pedestal Mode No (Operating speed) 1st speed (Hz) Margin in % Natural frequency (Hz) 1 74.311 62.5 18.89 2 91.026 62.5 45.64 3 138.48 62.5 121.56 4 151.50 62.5 142.40 5 163.01 62.5 160.81 6 166.70 62.5 166.72 7 206.90 62.5 231.04 8 250.40 62.5 300.64 9 269.06 62.5 330.49 10 276.61 62.5 342.57 The first natural frequency is increased from 63.25 Hz to 74.31 Hz. The percentage of margin between first natural frequency and operating speed is 18.89 % which satisfy the ANSI/HIS clause. It is evident that there is a significant increase in the frequency values mainly at the first mode after adding stiffeners to the pump pedestals under the pump feet. The variation of frequencies from original and modified design is shown in graph 1 Natural frequency (Hz) 300 280 260 240 220 200 180 160 140 120 100 80 60 40 20 0 Comparison of natural frequencies Original model Modified model 1 2 3 4 5 6 7 8 9 10 Mode numbers Graph 1: Comparing the natural frequencies ISSN : 0975-5462 Vol. 3 No. 8 August 2011 6343
Fig 11: Mode shapes with modified design 8. Conclusions: Application of vibration analysis technique for monitoring the centrifugal pumps are convenient and reliable in determining the failures in their early stages and can avoid unscheduled shutdowns and expensive repair costs. From the results of the FEA, it can be observed that how the dynamic characteristics of the centrifugal pump are improved. The increase of the stiffness of the centrifugal pump assembly will increase the frequency of the centrifugal pump. It is useful to guide design engineers to fix the problem to avoid the resonance. References [1] Singh, Y. P., Ball, J. H., and Rouch, K. E., "A Finite Elements Approach for Analysis and Design of Pumps," International Journal of Applied Finite Elements and Computer Aided Engineering, Finite Elements Analysis and Design, Vol. 6, pp. 45-58, 1989. [2] Jyoti K. Sinha and A. Rama Rao Vibration Diagnosis of Failure of Mechanical Coupling between Motor and Pump Rotors International Journal of Acoustics and Vibration, Volume. 10, No. 2, 2005. [3] Bernd durrer,frank-hendrik wurm, Noise sources in centrifugal pumps, Proceedings of the 2nd WSEAS Int. Conference on Applied and Theoretical Mechanics, Venice, Italy, November 20-22, 2006 [4] Cornelius Scheffer Pump Condition Monitoring Through Vibration Analysis Pumps: Maintenance, Design, and Reliability Conference, 2008. [5] Ravindra Birajdar [1], Rajashri Patil [2], Kedar Khanzode [3] Kirloskar Brothers Ltd., India,, vibration and noise in centrifugal pumps - sources and diagnosis methods 3rd International Conference on Integrity, Reliability and Failure, Porto/Portugal, 20-24 July 2009 [6] Giacomo Marenco, Alessandro Nicchio,Alberto Pivo.,Dynamic improvement of an overhung single stage pump, Proceedings of the twenty-fifth international pump users symposium,2009. [7] ANSI/HI 9.6.4-2000, American National standard for centrifugal and vertical pumps. [8] API standard 610, 2004, Centrifugal Pumps for Petroleum, Petrochemical and Natural Gas Industry, Tenth Edition, American Petroleum Institute, Washington, D.C. [9] Ansys help ISSN : 0975-5462 Vol. 3 No. 8 August 2011 6344