Modal Analysis as a Tool to Resolve Pump Vibration Issues John Koch HDR, Bellevue, WA jkoch@hdrinc.com ABSTRACT Vibration spectrum analysis and modal analysis are tools designers and plant staff can use to optimize their pumping systems. This paper specifically looks at the ways these sophisticated tools were used to diagnose and solve operational and mechanical issues on a two-stage raw sewage pumping station constructed in 1972 and upgrade twice since then to achieve its current 227 ML/d (60 mgd) design capacity. The modal and vibration analysis resulted in solving an intermediate bearing support structure issue, but uncovered other hydraulically induced vibration issues which will require additional investigation and study to resolve. KEYWORDS: Modal, vibration, Hydraulic Institute, pump, natural frequency, resonance INTRODUCTION The essential step in solving vibration problems is to understand resonance. High vibration levels can be caused by resonance in the rotating elements of the pump shaft, impeller or the motor rotor, in the structure of the pump and its volute, bearing housing or motor frame. Severe vibration, more appropriately defined as vibration above the Hydraulic Institute Standard (HI) recommended maximum limits as contained in ANSI/HI 9.6.4 can destroy bearings in pumps and motors as well as destroy mechanical seals. Resonance conditions in mechanical systems occur when the excitation forces coincide with the natural frequencies of the structure. A key to defining the source of the resonance is to determine if the source of the resonance is in the rotating elements of the pump or in the pump assembly including the pump base plate and supports and the structure the pump and pump base are attached to. To identify a resonance condition requires obtaining the operating vibration spectrums of the system and identifying the natural frequencies of the system. The rotating elements of a pump or motor can have a critical speed close to their operating speed; however, no rotating element is ever intentionally designed to operate in its critical speed or go through its critical speed. In my more than 45 years of commissioning equipment, there has only been one instance where the rotating element was the source of excessive vibration and that was a vertical pump s motor shaft which was excited by the variable frequency drive (VFD) carrier frequency. Figure 1 illustrates the excessive vibration of this installation. The vertical axis is inches per second-root mean squared; the horizontal axis is frequency in Hz. 298
Figure 1 Motor Shaft Vibration All other vibration issues that I have encountered have been attributed to excitation of the pump/motor structure. Most often when a pump s vibration exceeds HI limits, the issue is with the pump and its base not with its shaft. Almost all equipment in water and wastewater treatment plants are mounted on concrete equipment pads with grout poured in and under the equipment base as illustrated in Photograph 1. 299
Photograph 1- Grouted Pump Base Grouting the pump s equipment base provides damping to the pump and motor. Damping reduces the maximum amplitude of the vibration caused by resonance and in doing so can bring the equipment into compliance with HI maximum vibration limits. This is one of the reasons to make sure the equipment base is in full contact with the concrete equipment pad and all the air bubbles are expelled from the pourable grout mixture. The key tenet of resolving natural frequency issues is adding mass to a structure or stiffening the structure to move the natural frequencies out of the operating range of the equipment. Adding mass will typically lower the system s natural frequency; whereas, stiffening the structure of a rotating piece of equipment will raise its natural frequency. Photograph 2 illustrates where mass was added to a pump in an attempt to lower its natural frequency below the pump s operating speed. 300
Added Weight Photograph 2 Mass Added to Pumps Trying to do add mass and stiffen the structure most of the time is counterproductive. The formula for calculating the reed critical frequency or natural frequency is: Where k = stiffness and m = mass Experimental modal analysis is based on measured frequency response functions between a force applied to the structure and the response of the structure. The measured frequency response functions are post processed using modal analysis software to identify the natural frequencies of the structure. Accelerometers are used to measure the response of the structure and an instrumented hammer is used to apply the force to the structure as shown in Photograph 3. 301
Photograph 3 Impact Hammer to Determine Natural Frequency The natural frequency of a system is a property of the system that is defined by the inertial and elastic properties (mass and stiffness) of the structure. The inertial and elastic properties of a structure are a function of the material properties and the geometry of the components of the structure. Each natural frequency has a particular displacement pattern, called a mode shape, and each mode shape is independent of all other mode shapes of the system. To identify a resonance condition in pumping systems, the measured operating vibration spectrums are used to identify high vibration levels at the natural frequencies obtained from the modal analysis. The measured vibration spectrums are reviewed to identify any vibration levels that exceed the maximum allowable levels as defined by accepted industry standards. For components that have vibration levels above the maximum allowable levels, the vibration spectrum is inspected to determine at which frequency(s) the high vibration levels reside. Once the high vibration level frequency has been identified, it is compared to the results of the modal analysis to determine if there is a resonance condition. 302
As important as the stiffness of the pump and structure to reduce vibration levels below a HI maximum level is the hydraulic conditions at the inlet to the pump s impeller. American National Standard (ANSI)/HI 9.6.6 recommends a minimum of 5 diameters of unobstructed straight pipe into a pump suction unless a long radius reducing elbow with more than 50% area reduction is used. For a 300 mm (12-inch) pump suction this means a long radius 300 x 450 mm (12 x 18-inch) elbow would be required. Photograph 4 illustrates how dye in a standard radius elbow swirls into a pump inlet. Photograph 4 Standard Radius Elbow Comparing the standard radius elbow to the long radius elbow in Photograph 5, the flow stream is more uniform in the long radius reducing elbow than in the standard elbow. Turbulent flow into the eye of the pump impeller will cause unstable flow conditions and potentially high vibration levels in the pump. 303
Photograph 5 Long Radius Reducing Elbow BACKGROUND A 227 ML/d (60 mgd) two-stage high head, greater that 76m (250 feet) total dynamic head (TDH) raw sewage pumping station was evaluated for its problematic maintenance issues and perceived vibration problems. Several studies and attempts to resolve the issues were performed over the last 15 years including a hydraulic model study. The station was configured with the discharge of the first pump routed to the intake of the second stage pump. Photograph 6 illustrates the first and second stage pumps installed in the cramped pump room. 304
Photograph 6 - Two Stage Pumping Units Several of the maintenance issues in the pumping station were due to the tight quarters for performing any maintenance related activities. Many of the operational problems with the pumping units were the short suction piping and 90-degree fitting into the suction of these vertically configured pumps. The three different levels for pumps and motors presented both maintenance and operational issues with the units. Photograph 7 illustrates the motors on the next level above the pump room level. 305
Photograph 7 - Pump Motor Level The installation utilized a long shaft assembly between the two floors. The shafting is supported by intermediate guide bearings approximately half way between the two floors which are illustrated in Photograph 8. Photograph 8 - Intermediate Guide Bearing Supports 306
Pumps and intermediate shaft bearings were typically rebuilt and replaced every 12-18 months because of the failure of one or more of the components in each set of pumps. METHODOLOGY The initial vibration analysis for the two-stage raw sewage pumping station determined there were vibration issues with the intermediate bearing assemblies which could be transmitting a resonance vibration to the pumps below. The intermediate support bearing structure was a series of parallel 41 cm (16-inch) wide flange beams (WF16X26) and 30 cm (12-inch) (C12x20.7) cross support channel beams for each pump set as shown in Photograph 9. Photograph 9 - Intermediate Bearing Supports The multiple reference impact testing approach was used for this project where the response is measured at fixed locations and the forces are applied at all of the locations used in the modal analysis. Multiple reference impact testing is ideal for large structures like the intermediate bearing structure because it simplifies the measurement process allowing the frequency response functions to be acquired efficiently. 307
The intermediate bearing support frequency response function measurements were made using a Dytran Instruments Model 5802A impulse hammer and 3 PCB Piezotronics Model 604B31 triaxial accelerometers. For each measurement point the structure was excited with the hammer and 9 frequency response functions were measured. A total of 62 and 66 points were measured on the stage 1 and stage 2 intermediate bearing support structures respectfully. The measured frequency response functions were used to estimate the natural frequencies of the intermediate bearing support structures. The OROS Modal 5.2 modal analysis software was used to perform the modal analysis from the measured frequency response functions. For this project, the OROS BroBand modal identification module was used which is based on the Polyreference Least Squares Complex Frequency Algorithm. The modal analysis identified four modes (natural frequencies) of interest in the 0-100 Hz frequency range of the stage 1 and 2 intermediate bearing support structures. The operating speeds of pump sets 1-4 were 1800 rpm (30 Hz) and pump sets 5-12 were 1200 rpm (20 Hz). The modes of interest identified by modal analysis are shown in Table 1 and all are in or very close to the pump operating ranges. Table 1: Intermediate Bearing Support Natural Frequencies Mode Stage 1 (Hz) Stage 2 (Hz) 1 17.08 19.38 2 19.09 21.71 3 20.97 30.60 4 29.15 33.86 The mode shape for the Stage 1 structure s first natural frequency at 17.08 Hz is shown in Figure 2. The first mode is the center section of the intermediate bearing support which supports the intermediate bearings for Pumps 5-8 deflecting in the Y (horizontal) direction. Figure 2 - Stage 1 Mode Deflecting in the Y-Axis 308
The mode shape for the Stage 1 structure s fourth natural frequency at 29.15 Hz is shown in Figure 3. The 29.15 Hz mode shape in the Stage 1 intermediate bearing support is the structure deflecting in the X (north-south) direction while bending in the Z direction (vertically) in a wave fashion. Figure 3 - Stage 1 Mode Deflecting in the X-Axis Centrifugal pumps typically have two main sources of vibration as shown at rotating speed and at blade pass frequency. Pumps 1-4 operate at 1,800 RPM (30 Hz) and the pump impellers have 2 blades with a blade pass frequency of 60 Hz. Pumps 5-12 operate at 1,200 RPM (20 Hz) and the pump impellers have 3 blades with a blade pass frequency of 60 Hz. In Table 2, the first three rows show the operating frequency and the first two harmonics for both pumps. The last three rows in Table 2 show the blade pass frequency and its first two harmonics. Table 2: Pump Operating and Blade Pass Frequencies (Hz) Forcing Frequencies Pumps 1-4 Pumps 5-15 1X 30 20 2X 60 40 3X 90 60 1X Blade Pass 60 60 2X Blade Pass 120 120 3XBlade Pass 180 180 The maximum allowable vibration levels for the pumps, drive motors and intermediate bearing support were determined using the Hydraulic Institute standard 9.6.4-2009, ISO 10816-3, Technical Associates of Charlotte, P.C. criteria for overall condition rating and experience. The maximum allowable vibration levels were set at 8.64 mm/sec (0.34 in/sec) root mean squared (RMS) for the pumps, 5.08 mm/sec (0.20 in/sec) RMS for the intermediate bearing support, 4.57 mm/sec (0.18 in/sec) RMS for 74.6 kw(100 hp) drive motors and 7.11 mm/sec (0.28 in/sec) RMS for the 298 to 373 kw (400 and 500 hp) drive motors. 309
All of the overall vibration levels measured on Pumps 1, 2, 5, 6, 9, and 10 were compared to the maximum allowable. The results are shown in Table 3. The vibration levels, which exceed the maximum allowable levels in Table 3, are red and the levels that are close to the maximum allowable levels and warrant a closer look are highlighted in yellow. Table 3 - Measured Overall Vibration Levels Pumps 1, 2, 5, 6, 9, and 10 mm/sec (in/sec) RMS Location Pump 1 Pump 2 Pump 5 Pump 6 Pump 9 Pump 10 Motor X 2.79 0.25 1.02 2.29 2.54 3.56 (0.11) (0.01) (0.04) (0.09) (0.10) (0.14) Motor Y 1.52 1.78 1.02 3.05 1.78 3.56 (0.06) (0.07) (0.04) (0.12) (0.07) (0.14) Motor Z 1.02 0.76 6.10 0.51 0.76 1.78 (0.04) (0.03) (0.24) (0.02) (0.03) (0.07) Intermediate Bearing X 7.37 2.79 2.79 1.52 2.03 5.84 (0.29) (0.11) (0.11) (0.06) (0.08) (0.23) Intermediate Bearing Y 1.52 4.06 4.83 3.05 21.59 16.26 (0.06) (0.16) (0.19) (0.12) (0.85) (0.64) Intermediate Bearing Z 1.02 1.52 2.03 4.32 1.52 2.79 (0.04) (0.06) (0.08) (0.17) (0.06) (0.11) Pump X 4.32 8.89 10.92 12.70 4.06 14.48 (0.17) (0.35) (0.43) (0.50) (0.16) (0.57) Pump Y 5.08 4.83 7.37 5.84 7.37 3.81 Pump Z (0.20) 0.76 (0.03) (0.19) 1.27 (0.05) (0.29) 2.29 (0.09) (0.23) 4.83 (0.19) (0.29) 2.79 (0.11) (0.15) 6.35 (0.25) Pump 1 vibration levels are below the Hydraulic Institute maximum allowable levels at all locations and directions, except the intermediate bearing X direction at 7.73 mm/sec (0.29 in/sec) which is above the 5.10 mm/sec (0.20 in/sec) (RMS) maximum vibration level for the intermediate bearing. Figure 4 shows the vibration spectrum from the Pump 1 intermediate bearing. The dominant vibration level is at operating speed (30 Hz) of the pump. The modal analysis also identified a natural frequency of the Stage 2 intermediate bearing support at 30.64 Hz. The mode shape for the Stage 2 intermediate bearing support at 30.64 Hz natural frequency is predominately in the X direction. Based on these results, the high levels of vibration of the Pump 1 intermediate bearing are due to a resonance condition. 310
Velocity (in/sec RMS) WEF Collection Systems Conference 2017 0.5 Pump #1 Intermediate Bearing Support Vibration 0.45 0.4 X Direction Y Direction Z Direction 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0 20 40 60 80 100 120 140 160 180 200 Frequency (Hz) Figure 4 - Pump 1 Intermediate Bearing Support Vibration Spectrum Pump 2 vibration levels are below the Hydraulic Institute maximum allowable levels at all locations and directions except the pump in the X direction. The vibration spectrum for Pump 2 shows that the X direction vibration is dominated by the blade pass frequency at 60 Hz and 2 times blade pass at 120 Hz as shown in Figure 5. 311
Velocity (in/sec RMS) WEF Collection Systems Conference 2017 0.5 Pump #2 Vibration 0.45 0.4 X Direction Y Direction Z Direction 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0 20 40 60 80 100 120 140 160 180 200 Frequency (Hz) Figure 5 - Vibration Spectrum for Pump 2 The vibration at the blade pass and 2 times blade pass were below the maximum allowable vibration level of 8.64 mm/sec (0.34 in/sec) RMS. Pump 2 does not have any natural frequencies close to 60 Hz, which eliminates a resonance condition as the root cause of the high vibration levels. Pump 2 also shows signs of cavitation, which is an indicator of hydraulic issues with the pump, which will also increase the blade pass vibration levels. The cavitation induced vibration in the 60-90 Hz range increased the overall vibration level to 8.89 mm/sec RMS (0.35 in/sec RMS). The same analysis procedure was applied to Pumps 5-10 which, like Pumps 1 and 2, found the vibration levels that exceeded the maximum allowable levels on the pumps were due to hydraulic issues with the pumps and not due to resonance conditions in the pump structure. The high vibration levels on the intermediate bearing support on Pumps 9 and 10 were due to resonance conditions where the pump operating speed of 20 Hz was exciting the 20 Hz natural frequencies in the intermediate bearing structure. 312
RESULTS The modal analysis suggested that stiffening the intermediate bearing support structure would raise the reed critical speed of the supports. A finite element analysis was performed with the data from the modal analysis which determined that welding a 7mm (1/4 ) plate to the top and bottom of the longitudinal beam structure would provide the necessary stiffness to change the natural frequency of the support system. Photograph 10 shows the completed modifications to the beams. Photograph 10 - Modified Intermediate Bearing Support Structure After the suggestions to stiffen the intermediate bearing structures were performed by the City, another round of analysis of the entire pumping station was conducted to gather at one time the following information to try and pinpoint the operational and maintenance issues with this pumping station. The second round of vibration testing included: Vibration signature of each pump, intermediate bearing and motor. Flow from each two stage pump set measured with the stations flow meters that had been recently calibrated. Suction and discharge pressure from each pump measured with liquid filled calibrated pressure gauges at the appropriate pressure ranges and fitted with diaphragm seals. Power for each set of pumps measured at each motor starter. The maximum allowable vibration levels were determined using the Hydraulic Institute standard 9.6.4-2009, ISO 10816-3, Technical Associates of Charlotte, P.C. criteria for overall condition rating. The Hydraulic Institute Standard 9.6.4-2009 addresses the solids handling pump vibration levels but does not address the motor or intermediate bearing. Technical Associates of Charlotte 313
criteria addresses vertical pump based on the height of the motor above grade but not a solids handling pump specifically. Neither ISO 10816-3 nor Technical Associates of Charlotte specifically address the intermediate bearing support maximum allowable vibration levels. The maximum allowable vibration level for the intermediate bearing was determined from experience. Table 4 shows the maximum allowable vibration levels defined by the two (2) standards, (HI and ISO) Technical Associates of Charlotte and experience. The last column on the right in the table shows the maximum allowable vibration levels for this project based on the two (2) standards and experience. Table 4 - Maximum Allowable Vibration Levels (in/sec RMS) Location HI 9.6.4-2009 ISO 10816-3 Technical Associates of Charlotte Criteria used Motor 100 HP 0.18 0.18 Motor 400 and 500 HP 0.28 0.28 Intermediate Bearing 0.20 Pump 0.34 0.39 0.34 Vibration measurements at the intermediate support structure were recorded after the modifications were made by city personnel. The modifications had reduced the intermediate bearing vibration levels from 22.00 mm/sec (0.86 in/sec) RMS to 3.60 mm/sec (0.14 in/sec) RMS, considerably below the maximum allowable level of 5.00 mm/sec (0.2 in/sec) RMS. The City had achieved success in reducing the resonance frequency and vibration issues associated with the intermediate bearing support structure. DISCUSSION Vibration and modal analysis defined structural/mechanical issues with the two-stage vertical end suction pumps. Structural issues were resolved with the intermediate bearing support structure when the independent wide flanged beams were stiffened and modified to act as one large box beam as shown in Photograph 10. With this piece of the puzzle resolved, the hydraulic induced vibration issues can be further investigated. The vibration signature of all of the pumps, once the resonance from the intermediate bearing was reduced, was at blade pass and 2x blade pass frequency. Centrifugal pumps typically have a dominant vibration at blade pass frequency. Blade pass frequency is the number of impeller blades times the operating RPM. As an example a two bladed impeller operating at 1800 RPM (30 Hz) would have a blade pass frequency at 60 Hz (30 Hz x 2). Issues that contribute to blade pass vibration are: 1. Non-laminar fluid flow to the pump suction and impeller. 2. Net suction positive pressure required (NPSH3) exceed net positive suction pressure available (NPSHA). Or simply stated, the water level in the wet well is too low. 314
3. Pump operating outside of the pump s preferred operating range (POR) and/or to the far right of the acceptable operating range (AOR). Further detailed investigation and analysis of the data collected will be required to pinpoint the root cause of the continued hydraulic vibration issues with the raw sewage two-stage vertical end suction centrifugal pumps. CONCLUSION Modal and vibration spectrum analysis, while not the ultimate resource for diagnosing and resolving mechanical failures, are powerful tools to assist operation and maintenance personnel in determining some of the root causes of equipment failure. As was the case in the investigation of the two-stage vertical end suction pumps, one issue was eliminated; however, several other potential problems were uncovered. Vibration monitoring is a great evaluation tool that can be used to diagnose issues and problems. It can and should be a tool for acceptance of installed pumps to confirm they meet the minimum American National Standards Institute/Hydraulic Institute Standards. ACKNOWLEDGEMENTS The authors gratefully acknowledge the staff at the wastewater pumping stations for their patience while all of the issues were investigated and satisfactorily resolved. I also wish to thank the construction personnel that persevered during the issues with the suppliers and factory personnel as well as the hydraulic modeling laboratory for their continued help in evaluating pumping station hydraulics. Balancing Services Company and AVS Engineering, LLC are thanked for their continued assistance in diagnosing vibration issues with rotating equipment across the country. REFERENCES Hydraulic Institute (2009) Rotodynamic Pumps for Vibration Measurements and Allowable Values; ANSI/HI 9.6.4; Parsippany, New Jersey. Hydraulic Institute (2009) Rotodynamic Pumps for Pump Piping; ANSI/HI 9.6.6; Parsippany, New Jersey. Technical Associates of Charlotte, P.C. Vibration Criteria; Charlotte, North Carolina. International Organization for Standardization, 10816-3:2009 Mechanical Vibration, Geneva, Switzerland 315