Pumps and all types of pumping equipments use mechanical action to transport materials such as gasses and liquids. The transportation takes place from the area of low pressure to the area of high pressure. The most common type of pump which is used in our homes is the water pump. Water pump is a machine which can be used for increasing the pressure of water in order to move it from one place to another. Types of water pumps include reciprocating pumps, rotary pumps, centrifugal pumps, turbine pumps, jet pumps, and shallow well and deep water pumps. (Kietzman 2009). Modern water pumps serve a variety of purposes such as providing a water source for agriculture and have industrial, municipal and residential uses. They also aid in helping to move wastewater in sewage treatment plants.
Affects of Vibration
It has been estimated that 6 components of water pumps are seriously affected by vibrations of the pump such as:
Bearing Seals
This part is reacts very sensitively to the shaft radial movements. Thus the movements may cause the bearing seals to fail prematurely due to an increase in the damage of the shaft. It should be kept in mind that labyrinth seals have a very low tolerance.
Bolts
Vibrations may result in pump and motor hold down bolts to become loose.
Tolerance
Vibrations will also cause damage to wear ring clearance and impellar settings.
Causes of Vibrations in the Pump
By investigating the causes of vibrations in the pump, we will know how the main parts contribute to vibrations in the pump. Vibrations in the pump may be causes due to mechanical reason, hydraulic factors or other reasons which will be described later.
Mechanical Causes of Vibrations
Unbalanced Rotating Components. Damaged impellars and non centric shaft sleeves
Bent of wrapped Shaft
Misalignment of Pump and Driver
Piper Strain by Design or due to Thermal Growth
Because of the mass of the pump base, in case it is too small
Due to the thermal growth of various components, especially shafts
Rubbing Parts
Due to loose or worn bearings
Due to loose hold down bolts
Loose parts
When a product is attached to a rotating component
Damaged Parts
Hydraulic Causes of Vibrations
Operating off of the pumps BEF (Best Efficiency Point)
Due to product vaporization
Due to impellar vane running too close to the pump cutwater
Internal recirculation
When air is allowed to enter the system through vortexing etc
Because of turbulence in the system such as non-laminar flow
Because of water hammer
Apart from the mechanical and hydraulic causes, there can also be other causes of vibration such as
Harmonic vibrations from other nearby equipments may contribute to the vibration
Due to speed, when the pump is operated at a critical speed. This problem is especially common in pulley driven and variable pumps
Due to seal slip stick at seal faces, in case of pumping of non-lubricating fluid, a gas or a dry solid.
Vibration may also be caused a pump discharge recirculation line aimed at the seal forces
Chapter 2
Literature Review
The purpose of the literature review is to investigate the causes of vibrations in water pumps, how they arise and what methods can be used to control them.
According to R. Rayner, vibration may be caused by sources such as abnormal suction conditions, lack of proper lubrication, recirculation, when the pump is not properly designed, improper application of base plate and grouting procedures, lack of attention to coupling fitting, balance or key or when seals, fittings or flush cooling are improperly selected (Rayner, 1995, p. 203)
The above mentioned causes have been studied in detail in the literature of the report, However we will study them briefly here. Vibrations due to abnormal suction conditions usually because of dysfunction of the first stage impeller. Due to a deformity which will be studied in detail, this impeller starts absorbing vapor, and consequently the entire pump becomes vapor locked as the vapors not able to exit via the discharge valve. Thus the pump may become clogged and other damages also result.
Lack of lubrication is also a problem that is related to cavitation. The concept of cavitation will be studied in detail, but it is important to mention here that cavitation leads to vapor locking which inturn affects the capacity of the impeller to pump fluid. The bearings then becomes devoid of lubrication. This results in galling when they come into contact with the stationary parts. Cavitation can be avoided by ensuring that the Net Positive Suction Head Available, which displays the pressure in absolute terms at impellers eye, is always greater than what has been specified by the maker or the pump. (Haman, Izuno Smajstrla, 1989). NPSHa can be computed via the formula
NPSHA Barometreic Pressure Suction Head or Lift Friction Loss in the pipe Vapor Pressure ata given temperature (Haman et al., 1989)
We also know that the original seals and bearings is not able to handle vibrations effectively, therefore various modifications have also been proposed by various researchers. These modifications are designed to increase stiffness and damping capabilities. Since the center and throttle bushings were destabilizing, one method to increase the stability is to modify the seals especially the center bushings. When rotating rotor groves are removed, minimum clearance levels can be maintained for the entire length of the stationary bushing. This new annular seal when compared with the previous grooved seal has found to have more damping (50 more) and reduced cross coupled stiffness levels. Other readings involved logarithmic decimal values increasing to around 0.3 (we will compute later to show that positive log decimal values ensure stability of the rotor, while a value 0.3 log decimal should be maintained during normal running conditions) even at low aerodynamic loads, while the value still remained positive at even higher loads. When the performance of this pump with the modified rotor was compared with the other pump, it showed greater stability, thus it was recommended by the manufacturers that such modifications be done.
Chapter 3
Methods (Examining the Pump in Lab)
Previously we discussed the causes of vibration in water pumps and the adverse effects of vibrations on different mechanical components of the pump. Now we will attempt to explore how this vibration is caused, and which parts of the pump contribute to the vibration. Vibrations in centrifugal water pumps can be caused by both synchronous and non-synchronous ways. Synchronous ways of vibration include vane pass frequency energy and running speed energy, however vibrations due to non-synchronous ways result in more damage because of the inability to diagnose these issues due to the vagueness of exciting mechanisms which cause the vibrations. Non-synchronous ways of vibration include recirculation, stage hall and instabilities of the shaft.
Shaft
In machines, vibrations due to shaft may result when it is bent. In this case the shaft basically loses the power to rotate about its axis. The following experiment would help reveal the reasons for a bent shaft in a water pump and the associated vibrations which are caused. The reasons are basically attributed to upthrust forces which not only cause extensive vibrations but also result in bent shafts and vapor locking which affect seals and bearings. A series of tests can help demonstrate this effect, such as these field tests which were conducted on two pumps. The tests were conducted to obtain the following information
Flow rates
Parallel pump operation effects
How opening of the discharge valve affected the upthrust forces
The data was obtained with the aid of transducers, both fixed and temporarily incorporated transducers. The following data were obtained.
Suction Static and Dynamic Pressures
Both the static and dynamic pressures were recorded with the help of a transducer incorporated in the drain after upstream portion of the pump. A second transducer was incorporated inside the head of the pump. In this case the use of the transducer is similar to using a manometer which helps record the pressure at the pump section bell.
Discharge Static and Dynamic Pressures
In this case, the location of the transducer which will help measure the static pressure is just downstream of the pump at the location of the vent.
Pump Shaft Vibration
Installations of the proximity probes were done at the levels of mechanical seal and the bottom of the motor. The installation of these probes was done radially. The probes were installed in pairs, the two probes having a separation of 90 degrees from each other. These probes served two purposes, first it helped obtain the orbit of the shaft vibration and secondly shaft centerline positions could also be determined. To calculate whether the direction of the shaft impulsion is upstream or downstream, a third probe was installed which was positioned vertically to the other two probes.
Suction temperature in pump barrel
Heat temperatures in the pump barrel were calculated with the aid of a thermocouple which was incorporated in the drain of the pump barrel.
Vibration of Motor and Pump Housing
In order to measure vibrations of motor and pump housing, triaxal accelerometers were put on top of the motor and the head of the pump discharge. This helped in calculating the direction of the vibrations resulting from the structure.
Motor Current
Clampon amp probes were used for this purpose.
Flow Rates
The equipment which was installed in various portions of the pump helped calculate the monitor and calculate the flow rates.
Motor Speed
For this purpose an optical tach was used.
All the information which was obtained as a result of the field tests were recorded by using a 32-channel digital tape recorder. Other equipments which were used include a spectrum analyzer which was used for drawing spectrum plots. Time domain data were obtained from analog to digital convertor and proprietary software was used to control both the equipment and help in acquiring the data.
Pump 1 1st Start with Discharge Valve Fully Open
Discharge valve was kept fully open before starting this pump. Venting of the pump was also completed before the pump was started. This venting procedure is used to remove vapors and ensures that the liquid in the system is full. The bypass valve around the recycle valve was slightly opened after closing the recycle valve. Increasing the suction pressure in the pump can by 100 psi lifted the pump shaft vertically to about 20 mils. All this had happened before the pump had started operating. However, according to the producer of the pump, this behavior was not uncommon. It resulted mainly because the unbalanced force on the pump shaft was larger than pump rotors weight itself. Thus the motor was in an upthrust position when the pump had started.
Full speed was reached in 1.75 seconds. As with the case of the discharge pressure it showed a gradual increase and required a time of around 30 seconds to move to the point of 400 psi. No flow was thus indicated till 20 seconds after the start of the pump. A maximum flow rate of 1200 gpm was achieved after an interval of 30 seconds which resulted in the pump to trip. This flow rate seemed inappropriate since it was even higher than the maximum flow rate of the pump. It might be that this discrepancy had occurred due to vapor in the piping of the pump which resulted in an incorrect reading of the flowmeter
This upthrust condition was maintained for about 25 seconds and till the discharge pressure had increased to about 200 psi. It is this upthrust condition which can cause bending of the shaft, thus leading to vibrations in the pump. Thus it needs to be avoided.
Pump 1 2nd Start with Discharge Valve Fully Open
Before this pump was restarted again, the runout of the pump was measured by pressurizing the barrel of the pump. Thus it meant that the shaft was in the upthrust position. The runout had increased from 7.5 mils to about 12 mils. It was revealed that the bending of the shaft was just temporary which was caused by the shafts upthrust position.
It took a time of around 25 seconds for the pump to reach a pressure of 500 psi which showed that the discharge pressure increased only gradually. 850 gpm was the highest recorded flowrate. It might be that this was the actual flowrate. Data revealed that the flow rates were correct, since the current data of the motor was not constant. Also the motor amps were somewhat reduced during this period of high flow rate. An upthrust position was maintained by the shaft until the pressure reached above 200 psi. This position was maintained for about 15-20 seconds. As the discharge pressure increased above 200 psi, the vibration on the shaft started to decrease. This was because the downthrust of the pump increased with a higher discharge pressure. We know that when the shaft is in tension, the pump should operate in downthrust.
Pump1 Pump Startup with Slight Closed Discharge Valve
The previous tests helped to reach the conclusion that the startup of the pump should be done with a partially closed discharge valve. This will also help to achieve the required pressure in a shorter period of time, thus reducing vibration. It took the pump only 1.5 seconds to reach its full speed. The discharge pressure also reached 350 psi in just about 1 second. Because of the partially closed discharge valve only a period of 0.5 second was taken by the pump to change its position from upthrust to downthrust. With the discharge valve fully open this time period ranged from 15-25 seconds. The vibrations of the shaft were found to be greatly less when position of the pump was changed from upthrust to downthrust. Here the vibrations remained largely the same over a large flow range before the pump switched to a downthrust position.
Thus to reduce the shaft vibrations caused as a result of upthrust forces it was recommended that the pump should be started with an almost closed discharge valve. Gradually opening the valve after a few seconds of operation helped ensure that the pump operated with constant vibration levels.
Pump 2 Start with pump 1 running
This was a new pump with all parts being unused such as a new first stage impellar and Graphalloy Thus it contained new parts except for a few column bushings.
Before starting the pump, the shaft was rotated manually by hand and the runout which was measured at the mechanical seal was about 4 mils without any suction pressure. With 180 psi suction pressure this runout was increased to about 12 mils in the upthrust position. The increase was attributed to compression of the shaft in the upthrust state.
This pump was turned on while the 1st pump was already running. Since the first pump was already running, this pump was started with the discharge valve fully open. Downthrust position was achieved after 0.5 seconds of startup. The discharge pressure increased quickly as the pump achieved full speed. The vibration levels reduced form 9 mils to 4 mils after the downsthrust position was achieved.
After 9 seconds of start of the 2nd pump, the 1st pump tripped off. After tripping, the axial position of the 1st pump switch to upthrust as the discharge pressure was lessened to the level of suction pressure.
When this pump was turned off, level of vibration increased to about 11 mils during the coastdown when the upthrust position was reached. The vibration calculated in the upthrust position before the pump was started was the same as this shaft vibration. This indicated that the shaft had not bent during the operation.
Conclusion of the Tests
Using the measured data at hand, technical references and after evaluating the failed pumps, the following conclusions can be drawn
High shaft vibrations were produced when the pump was operated with discharge valve fully open. These high vibrations contributed towards bending the shaft. This resulted because the shaft operated with high vibration levels in the upthrust position for a period of 15-25 seconds.
When the discharge valve was fully closed, the shaft did not become permanently bent. This was because the upthrust position in this case was maintained for a period of only 0.5 seconds.
However when the pump was started with the discharge valve fully open while another pump was in service yielded good results. This was because of the pump was started against a high discharge pressure.
No record of cavitation was observed. This meant that vapors were not being produced in the pumps as a result of cavitation at the impellars.
The data from proximity probes revealed that at specific conditions the shaft was deflected radially. This resulted in the shaft being forced against the bushings. It is believed that this force against the bushings would increase when the shaft is bent. This increase in the force against the bushings due to bent shaft resulted in higher temperatures at the bushings. This heat can then result in the liquid to vaporize. In the absence of a vent system, this production of vapors could result in vapor lock at the impellars. Finally the pump could also fail as a result of lack of cooling.
When the field tests were conducted, the vent systems were also installed in the pumps. However, no increase in incidence of rising temperature levels was recorded. This showed that vapors were not being collected.
Vibrations increased to high levels as a result of the shutdown. This resulted because the shaft remained in the upthrust condition for a period of 25 seconds as the pump was coasting down. It is thus important to reduce shutdowns which could help prevent seal wear.
Shaft vibrations were greatly increased when the pump was allowed to operate in the upthrust condition. The prior failure of seals was also attributed to this fact.
Altering the startup procedures helped in eliminating such failures.
The field tests also revealed that only vibration levels at the shaft should be used as a standard to evaluate vertical pumps as compared to vibrations at the motor and pump discharge housing. This is because vibrations at these areas remained low even when the shaft vibrations were high.
Thus the field tests illustrated here how the upthrust forces contribute to the shaft being bent which inturn increases the vibration.
Bearings and Impellar
Vibration at bearings is the root cause of most vibration problems in mechanical devices. The problem usually starts here and later spreads to every part. The root cause of vibrations produced as a result of bearings and impellars in pumps is the phenomenon of cavitation. This process is explained as under
Because of low pressure, the volume of liquid may burst forming a cavity. When vapor gases start evaporating into the cavity from the vicinity, the cavity no longer remains a perfect vacuum but it has a perfectly low gas pressure. Thus due to this pressure difference (between the surrounding and the cavity), the bubble collapses. Temperature and pressure inside the bubble are elevated. A lot of energy is released as a result of this collapse as the gas inside the bubble spreads into the nearby liquid. At this point the temperature may reach up to several thousand Kelvin and the pressure may soar to several hundred atmospheres. Thus this whole process may result in destabilizing forces to act on the impellar and result in high vibrations of the rotor.
In pumps there are two form of cavitaion which are produced, discharge cavitation and suction cavitation. (Dowson Taylor 1979, p.35)
Suction cavitation is a low pressure high volume condition where the liquid first turn into a vapor. This vapor however is unable to discharge itself from the impellar because of the absence of vacuum. It is then converted back into the liquid. This can have great impact as it damages the face of the impellar. It may either have large chunks of material being removed from its face or small pieces. Thus impellar may end up having a sponge like appearance. In both mentioned cases the end result is premature impellar failure which will occur as a result of bearing failure. This form of cavitation can be identified with a gravel of marbel like sound emerging from the pump casing. The other form of cavitation (discharge cavitation) usually happens in instances when the pump is performing its operations at 10 of its BEP (Best Efficiency Point, for BEP calculation see page 35). Under these conditions, the discharge pressure is very high resulting in the fluid recirculation inside the pump as it is not able to exit the pump. As the liquid flows around the impeller, it must pass through the small clearance between the impeller and the pump housing at extremely high HYPERLINK httpen.wikipedia.orgwikiVelocity o Velocity velocity. This velocity causes a vacuum to develop at the housing wall (similar to what occurs in a HYPERLINK httpen.wikipedia.orgwikiVenturi_effect o Venturi effect venturi), which turns the liquid into a vapor. A pump that has been operating under these conditions shows premature wear of the impeller vane tips and the pump housing. In addition, due to the high pressure conditions, premature failure of the pumps mechanical seal and bearings can be expected. Under extreme conditions, this can break the impeller shaft. This form of cavitation can be identified with the sound similar to knuckles cracking.
As discussed earlier vapor locking of the impellars of the pump may also result in lack of lubrication at the bearings. This happens usually when the first stage impellars starts absorbing huge amounts of vapor. It results in small vapor bubbles passing through the impellers. This large amount of vapor can reduce the ability of the impellar to pump fluid. This starts a vicious cycle because the subsequent impellars also become vapor locked due to lack of flow of fluid into them. This process continues until the entire pump becomes vapor locked. Vapor locking can be avoided by continuously venting the pump barrel. Thus vibrations due to bearings are produced as a result of a disability of impellars to pump fluid because of whole process of cavitation. Without proper lubrication the bearing would gradually deteriorate and fail, but before the fault is detected, this results in the damage of other parts of the machine. Thus lack of lubrication at the carbon bushings produce heat which can result in the failure of these bushings. This can cause galling between the stainless steel parts because the wear rings on the impellars are now in direct contact with the stationary parts.
Chapter 4
We have demonstrated in our discussion the impact of upthrust forces that is how they contribute towards vibration which not only causes bent shaft but also cause damage to the seals and bearings. In specific cases, upthrust forces may also cause pump failure. Several solutions are therefore proposed to deal with the problems associated with these upthrust forces.
Hydraulic Analysis should be performed by the maker of the pump. This is necessary in case the running conditions such as flow rates, discharge and suction pressure are changed or fluid properties (such as specific gravity) vary significantly from the original values.
In a situation where the pump is running alone, it should be started with the discharge valve slightly closed. After the discharge pressure is fully developed after a few seconds this discharge valve can then be fully opened.
However in a situation where another pump is also running, the discharge valve can be kept fully open. The reason for this is that in this case the pump will be started against a high discharge pressure.
Effort should be made to lessen the number of startup and shutdown times. This is because of the upthrust conditions which exist for a short period of time during startup and shutdown of the pump. This effect has been demonstrated in the field tests which were discussed earlier.
In order to get an accurate picture of the extent of shaft vibrations proximity probes should be used instead of velocity transducers on the motor pump thrust stand. The latter is an ineffective way of measuring upthrust problems. Additional proximity probe could also be installed located axially to calculate upthrust.
Apart from upthrust forces, vapor locking which causes lack of lubrication at the bearings can also be reduced by creating proper venting mechanisms and certain design modifications.
To prevent vapor locking proper venting of the pump barrel is imperative at the auxiliary and seal components. Other than water pumps, this process is important in all the pumps, especially for liquids which are near the vapor pressure such as LPG because they evaporate quickly and hence can easily result in vapor locking.
Venting of the pump barrel should also be done continuously to the vapor side of the suction vessel with liberal size piping.
Apart from this above mentioned piping modification, other modifications which are proposed to reduce this instance of vapor locking. The purpose of these modifications is primarily to reduce cavitation which could inturn result in vapor locking. Cavitation basically means formation of vapor bubbles which occurs when the pressure of the liquid falls below the vapor pressure.
In order to lessen the Net Positive Suction Head Required (NPSHR), it was proposed that the diameter of the first impellar should be larger.
The original carbon bushings should be replaced with another Graphalloy nickel impregnated carbon bushings.
In order to prevent the pump from operating in a condition of low flow rates, an instrumental modification was proposed. This involved adding another instrument on the motor switch gear to enable the plant Distributed Control Systems to monitor the motor currents. Logic modification was added to the DCS which enabled the plant to trip in instance when the motor amps were operating below the minimum flow rates.
Another modification involved installing nickel bronze wear rings in place of the pumps stainless steel wear rings. Such a replacement would reduce the likelihood of galling.
Other modifications were proposed to reduce the impact of destabilizing forces at the rotor. These include
Air Injection
During the tests there was a perception that the cavity behind the impellar was serving as a bearing or a seal which were contributing to the destabilizing forces. These forces were very strong and caused the rotor to become unstable. Thus in an effort to lessen the effects of pressure forces in the cavity behind the impellar, tests were conducted. The tests involved allowing air to enter into the cavity which immediately put an end to the vibration. The idea was to decouple the fluid from the rear end of the impeller shroud. This helped in ending the rotating pressure field.
Despite the usefulness of this method to terminate the vibration, it was not considered feasible due to certain operational restrictions.
Increasing the Wear Ring Clearance
In this technique the pump was elevated to establish if the instability vibration would be affected as a result of the increase in clearance between the impellar and the wear ring. This also helped end any consequence of the wear ring and the impeller rubbing together. These proposed changes when put into affect did not yield favorable results. At supersynchronic frequencies, the increase in the ring clearance had no affect on the amplitudes of vibration.
Stationary Spoilers
The purpose here was to try to break the rotating pressure field at the back of the impellar. For this purpose spoilers or 8 small stationary ribs were incorporated on the pump case. This whole process was done without dismantling the pump. The spoilers were just fixed to the housing. Spoilers were limited to a height of about 38 inches because of space issues. Data which was obtained at the spoilers showed that the backward mode vibrations were attenuated. The point of differential pressure where the instability happened was increased it was increased from 19-25 feet. The fluctuating levels at the backward state were still large. Thus it was believed that by raising the height of the spoilers or increasing the number which are installed, effectiveness of the spoilers may be increased to cope with the destabilizing forces.
Prior experiments revealed that when clearances at the back of housing and the impellar shroud are reduced, the pressure created by the impellar rises sharply. These tests were performed with a spacer with 24 radial grooves. These grooves had direct affect of lessening the tangential speed in the leakage annulus, thus reducing the cross coupling hardness in the same manner as the stator roughness in a damper seal. The tangential velocity was also reduced, in the same way as in the grooves. Thus this process had the effect of reducing the impact of destabilizing forces.
Expeller Vanes
This process involved implanting of the small vanes at the rear end of the impellar. The purpose here was the same as in above experiments such as to reduce the impacts of destabilizing forces on the rotor. The expeller vanes could serve here to reduce the pressure difference formed across this impellars rear end, thus helping to lessen these destabilizing forces.
Space restricting led to dismantling the pump, without which this installation process would not have been possible. The space restrictions also restricted the height of the installed vanes, because of the clearances. Thus specially formulated vanes were developed for attachment to the impellar shroud. Data collected after this attachment of the vanes revealed that the instability vibrations were eliminated. Thus the solution for the problem of the destabilizing forces was established. This discovery was made an unchanging modification. There was some concern about the loosening of the bolts which were used to fix the vanes, however no such problem has yet arisen and functioning of the pumps seem to be smooth.
Chapter 4
Results
Calculations
Allowable Vibration Levels
Allowable levels of vibrations for vertical pumps have been prescribed by API Standard 610 (1995). The allowed vibration levels on the pump thrust bearing housing are 0.2 in per second root mean square (rms) and 0.3 in per second zero per peak. The following equation is used in calculation of these allowable vibration levels.
A 10,000 N
Au unfiltered displacement determined by the Fast Fourier Transform (FFT), mils peak to peak (not e 4.0)
N root mean square
We can approximate the allowable vibration levels with the help of this equation to equal 2.4 mils peak-to-peak at 1795 rpm and 1.7 mils peak-to-peak at 3570 rpm.
Calculating Net Thrust Forces
The net thrust forces are due to the both upward and downward forces which are acting on the pump
The downward forces emerge as a result of unbalanced pressure forces as well as because of the weight of existing parts
Upward forces emerge as a result of flow through the impellars caused by a change in momentum.
A simplified model will be presented here to determine these forces. However this model can be altered depending on the type of pump and its working.
Downthrust Force
Downthrust forces result because of unbalanced forces across the impellar. Suction pressure acts on upper and lower impellar shroud and discharge pressure acts on the impellar eye. By using the equation formed by Dufour and Nelson in 1993, these downthrust forces can be calculated. It has been observed that the highest downthrust level exists at the pumps shutoff position due to the higher head of the pump.
Fd ((constant)(H)(SG)) Rotor Wt
Fd Downthrust, lb
H Head, ft
Constant (Net eye area)2.31, lbft
SG Specific Gravity
Rotor Wt Total weight of shaft and impellars in lb
Upthrust Forces
The fluid passing through the impellar can produce the upthrust force because of the change in its momentum. By calculating the kinetic energy, V (2g), of fluid, these upward forces can be determined. As the velocity of this fluid which flows through the impellar increases, the upthrust forces also increase. This is why we see that these upthrust forces become really high as flow rates increase to high levels.
The following equation is used for calculating upthrust forces in case of fully radial flow. Upthrust forces in mixed flow impellars can be computed by multiplying the following equation with a value between 0 and 1, depending on the extent to which flow becomes radial. Axial flow impellars do not result in upthrust forces.
Fu 1 c ( Ve 2g) Ae
Fu Upthrust, lb (N)
Ve velocity in impellar eye, ftsec (msec)
g 32.2 ft sec (9.81m sec)
c Unit Conversion Constant, 2.31 for USCS, 1.02 for SI
Ae net eye area in cm
Calculations for Computing Axial Forces with the Help of Impellar Thrust Factors
Usually a hydraulic constant is provided by K for each impellar type which is the Hydraulic Thrust Factor. BEP that is operation at Best Efficiency Point is used to compute K. Best Efficiency Point can be calculated as follows
E whp bhp x 100, here
whp water horsepower
bhp break horsepower
However this method does not provide an exact value, because upthrust forces vary with the capacity. This component is unable to account for such factors. Thus thrust-capacity curves are usually used by the pump manufacturers to compute the impellar thrust. For example,
K is read from the curve and given root mean square value. K value attributes both upthrust and downthrust forces.
Then K (total pump head times specific gravity of liquid)
Discharge pressure should be lessened above the impellar eye with the help of balancing holes and rings in case the impellar thrust is very high, thus hydraulically balancing the pump. This helps in lessening the K value.
Increasing Shaft Stability by Using Pumpout Vanes
In this part computations show measurements which were done for the solution of super synchronous shaft vibration problems in centrifugal water pumps. At low discharge pressures, centrifugal water pumps were marginally stable however they became unstable as the pressure increased. As discussed earlier pumpout vanes were incorporated on the back end of the impellars to solve the vibration problem. These vanes were incorporated in a two stage centrifugal slurry pump. This pump was a installed as a coke crusher pump in the refinery. It had unshrouded (open) impellars. The performance data of the pump are shown as shown
Excessive shaft vibrations were experienced by the pump during shop acceptance tests of the pumps operation in water. This high level of vibration also resulted in contact of the pump with other stationary parts, particularly the centre bushing and the inward bearing housing seal. It was observed that the shaft frequency was 1.3 running speed, that is 4800 cpm while the pump was operating at 3600 rpm. Such vibration level was not routine.
Impact Testing To Measure the Rotor
Mechanical Natural Frequencies
Dry rotor natural frequencies were measured with the help of impact tests. The purpose was to determine the cause of vibration at 1.3 running speed. The rotor was mounted on the balance stand after being removed from the case. A significant response was indicated via the impact test at around 1.5 times the running speed. This was brought about by impacting one of the impellars parallel to the shaft. It was determined via the computer analysis that the response near 1.5 times running speed was not a natural frequency of the impellar but a natural frequency of the pump rotor.
Effect of Added Stiffener Vanes
Since it was believed that the previously measured effect was the result of high vibration, five stiffener wanes were incorporated to the rear side of the impellar in an attempt to raise the mechanical natural frequency of the impellar more above the running speed. Subsequent testing with the incorporated vanes revealed that vibration levels were eliminated which were present before 1.3 running speed. New modified impellars were developed, after the previously encouraging results. These had the same stiffner vanes as before but a thicker back plate. This did not yield fruitful results and the vibration elevls again became high at 1.3 running speed. Tests were again performed with the previously incorporated five stiffener vanes, which again showed that vibration levels were non-existent 1.3 running speed.
It was believed that the stiffener vanes helped lessen the pressure drop across the centre bushing and it is thought that they may have also reduced the aerodynamic loading on the impellar blades. Thus the stiffener vanes worked similar to pumpout vanes. It was however not possible to establish the difference between these impellar vanes and the modified version which was incorporated later with a thicker back plate. However it was believed that the difference could be attributed to welding of vanes to the rear end of the impellar. When the vanes were incorporated first, a sharp angle was formed between the vane and the impellar. The modified impellars had full bead welds on sides of the vane resulting in a smooth fillet on each side. Thus due to the advantage of the sharp angle which the original vanes had, they may have been more effective as pumpout vanes.
Stability Analysis
It was determined that the vibrations which were being caused at 1.3 running speed were due to rotor instability problem. There was a need to determine whether the vibrations were being caused by self excited mechanism or if it was the result of high pulsation forces. Proximity probes and piezoelectric dynamic pressure transducers were used for this purpose. Shaft vibrations were measured with the help of proximity probes and pulsation was measured with pressure transducers. Piezoelectric dynamic transducers were incorporated in the pressure tap areas in the suction and discharge piping and to centre of bushings and throat bushings in the seal flush lines.
The data which was obtained revealed that the pump became unstable as full speed was reached and the discharge pressure was raised. According to the data at specific running conditions, which were away from the Best Efficiency Point (high pressure, low flow low pressure, high flow), the rotor became unstable and circled in the forward direction. Frequency analysis showed that instability frequency near 1.3 running speed resulted in increased vibration levels. Vibration was also increased as the pump operated away from BEP. At the center bushing, the pulsation data correlated with the shaft instability vibration. It was difficult to determine at that time whether the vibration was being caused by pulsation or if pulsation was being caused by vibration at instability frequency. However later it was established that vibrations at 1.3 running speed were occurring as a result of self excited rotor stability. This meant that at the instability frequency pulsation was the result, rather than the cause of shaft vibration.
In self excited rotor dynamic instabilities, the rotor will circle at a frequency which is near a rotor lateral natural frequency. The instability vibrations will be subsynchronous (less than the running speed) in case the rotors function above the first lateral natural frequency. It will supersynchronous (above the running speed) in case the rotors function below the first lateral natural frequency.
These self excited instability vibration levels can increase further until they are limited by some non-linear effect, or until a rotor is able to contact some other part such as seals or center bushings. Differential loading on the pump impellar blades were supplying the energy for the instability vibrations. The pump is impelled to circle in the direction of the rotation because of this differential loading on the blades which creates cross coupling forces. Thus Kxy, which are known as cross coupling stiffness coefficients are produced by these cross coupling forces. The formula used to calculate these coefficients are shown below, which was later altered for use with centrifugal compressors.
Kyx -6300 (HP) (MW) N d h x ds
HP horse power
MW molecular weight
d discharge density
s suction density
N speed, root mean square
D impellar diameter
h minimum restrictive dimension in flow path
This equation will be modified for our use and application in centrifugal pumps. The term aerodynamic loading will be used in this case, even though we are not dealing with gas here. This is because originally the forces were applied to turbines and compressors where the loading was termed as aerodynamic loading. Thus to compute the aerodynamic cross coupling can be estimated as follows
Kyx -6300 (HP) N D h
Basic Concept of Rotor Stability
We can think of instability as a free vibration of a system having a negative damping.
Free vibrations disappear in a system of positive damping as soon as the exciting force is removed. However in a negative damping system when the vibration is initiated by such disturbance it grows without being limited.
Mathematically, instability can be shown as
mx cx kx0
This is called the differential equation of motion, here
k stiffness
c damping constant
m mass
x displacement
The solution for this formula is
x e-(c2m)t eiwt
or x e-(c2m)t (A cos t B sin t)
When amplitudes of vibration x1 and x2 occurring n cycles at times tt and t2 are compared, the dampening systems can be analyzed. Thus the above ratio is reduced to
x2 x1 e-(c2m)t
However if the quantity
e-(c2m)t 1
Then the vibrations will increase with the time as shown above
Therefore if ct2m 0, then the vibrations will be unstable. We define c2m as , the growth factor.
The logarithmic decrement (log dec) is defined as
c2mn , for small , then
2pi, therefore the log dec can be written as
2p -2pi n -f
The above is a convenient form of logarithmic decrement relationship as the eigen values for the damped critical speeds have the following form
s i, here
whirl frequency
growth factor, 1sec
Because here is positive, log decrement for a stable vibration (0) will also be positive. We see that theoretically rotors which have a positive log decrement value are stable. But under normal running conditions, logarithmic decrement should be about 0.3 for the entire rotor with the impact of the seal established at full load condition (full aerodynamic loading). This will help make sure that the rotor is stable under such conditions. For logarithmic decrement values between 0 and 0.3, the rotor is considered as marginally stable.
Rotor Stability Analysis
A computer program which used Myklestad-Prohl process was used for the stability analysis. Dampened eigen values and growth factors were computed.
We have mentioned in the literature review above of the modifications in the bearing to increase stability and the accompany increase in log decimal values that result. The following tables show the comparison of performance when the grooved seals were replaced by annular seals (Smith, D.R, Price, S.M. Kunz, F.K)
Table SEQ Table ARABIC 2 Comparison between Grooved Seals and Annular Seal Performance
Kxx (lb ftin)Kxy (lb ftin)Cxx (lb f-sin)Cxy (lb f-sin)Mxx (lb m)Grooved Seal PerformanceCenter Bushing (H2O)10,50011,60013.01.21.5Center Busing (HC)8,6009,60011.51.61.5Throttle Bushing (H2O)6,1003,4007.80.70.6Throttle Bushing (HC)4,8002,7007.30.50.6
Kxx (lb ftin)Kxy (lb ftin)Cxx (lb f-sin)Cxy (lb f-sin)Mxx (lb m)Annular Seal PerformanceSmooth Center Bushing (H2O)22,5006,00019.50.70.5Smooth Center Busing (HC)19700590019.40.60.4Smooth Throttle Bushing (H2O)8,5002,00010.80.20.2Smooth Throttle Bushing (HC)6,400 2,00010.80.20.2Source Adopted from Smith, D.R, Price, S.M. Kunz, F.K, viewed December 27, 2009 www.engdyn.compapersabstractsab75.htm
We see now that rotor instabilities were the cause of supersynchronous vibrations. Also because of little damping which was given by the anti friction bearings, the rotors were marginally stable. Cavities were responsible for producing the destabilizing forces which resulted in the vibrations. These cavities were formed between the impellars and the pump housing. Both backward and forward instability rotor vibrations were generated by these forces. Two theories have been formed to account for this instability, since it remains uncertain if pulsation (inside cavities at the back of impellars) caused vibration or if it was the other way around.
Theory 1 Because of the pressure wave which forms in this cavity, an impellar is provided with a force and thus causes rotor to vibrate. Various methods have been discussed above to reduced the impact of this instability such as with pumpout vanes by lessening the pressure in the area, with spoilers by lessening the tangential velocity of the fluid or with the help of air injection. The aim is to reduce the pulsation waves that will inturn aid in lessening of rotor instability.
The theory has some weaknesses. Firstly it does not account for why the pulsation was formed in the first place inside the cavity. Secondly it also does not help explain why the pulsation spread forward and backward.
Theory 2 Cross coupling forces on the impellar may be generated by cavities at the back of pump impellars when they act as seal or bearings. The extent of the force is determined by the dimensions of the cavity which impact clearances amid housing and impellar. All techniques described above such as spoilers, pumpout vanes and air injection helps in lessening the cross coupling forces, thereby directly subsiding the rotor instability. Pumpout vanes also aid in the reduction of the differential pressure across the cavity, this further helps in the diminishing process. A similar effect can be achieved by lessening differential pressure across the seal. The analytical support to such theories cannot be computed, since the current techniques are insufficient to examine characteristics of cross coupling forces in the ring cavity.
It is not necessary for a direct contact between rotating and stationary components to occur for backward rotor instabilities. Destabilizing pressure forces at the rear end were enough to produce backward and forward shaft instabilities.
For both horizontal and vertical pumps, the stability of the shaft can be established by using the stiffness and damping coefficients (for both bearings and seals). Horizontal and vertical pumps were receptive of pressure forces at the back of impellars (since they had low logarithmic decimal value).
Quoted stiffness for the bearing alone is greater than the actual effective bearing stiffness for antifriction bearings. The effective bearing stiffness since bearing is supported by the combine stiffness of the bearing housing and the pedestal.
We can see that the rotor may circle at subsynchronous and supersynchronous frequencies, since the centrifugal pump rotors are sensitive to the destabilizing effects of seals. According to the analysis stability of smooth seals is greater than grooved seals. When the grooves on the rotating seals were lessened, the destabilizing cross coupling stiffness (Kyx and Kxy) was reduced and direct damping coefficients (Cxx and Cyy) was increased. Thus not only the rotor stability was increased but also the effective stiffness of the shaft was increased.
Antifriction bearings help lessen the damping values in comparison with journal bearings. Destabilizing forces which impact on the rotor result in both subsynchronous and supersynchronous vibrations. Various methods have been proposed to manage this instability. This can be done by either increasing the rotor stability or reducing destabilizing forces. Various methods have therefore been proposed which have been discussed above such as with the help of pumpout vanes, stationary spoilers and air injection.
Apart from the destabilizing forces which affect the rotor stability, upthrust forces also contribute to the vibration in pumps, cause bend shafts and sealsbearings damage. A direct link exists between the position of the discharge valve and the impact of these upthrust forces. Various methods have therefore been proposed when operating the pump o avoid the effect of such forces which contribute towards vibration. A hydraulic analysis should be performed by the pump manufacturer. Also when a single pump is operating, the discharge valve should be kept partially closed which can be opened after a few seconds of operation when the discharge pressure has been fully developed. In case of parallel operation with another pump, discharge valve should be kept fully open as it will be started against a discharge pressure in this case. Reducing the number of startups and shutdown will help minimize these forces as test has indicated upthrust conditions occur during this period. Proximity probes should be used for calculating shaft vibrations as shaft vibrations are difficult to detect with other forms and equipment.
Affects of Vibration
It has been estimated that 6 components of water pumps are seriously affected by vibrations of the pump such as:
- Mechanical Seal.Movement of the shaft and mechanical seal are directly related. Carbon face chipping and seal face opening are consequences of vibration. Vibration will also cause wearing of the drive lugs and effect seals of metal bellows. Inside of the stuffing box may also come into contact with the rotating seal components or any other object due to vibrations of the pump. This will cause opening of the faces of the seals and solids will be able to enter the lapped faces and cause damage. When set screws become loose and slip on the shaft, this may cause the lapped seal faces to open.
- Packing.Radial movement of the shaft can directly affect the packing of the pump. Large leakage and large sleeve or shaft wear are the consequences. Because of the high friction of the packing, more flushing will be necessary to make up for the heat.
- Bearings.This part serves the purpose of handling both axial and radial load. Bearings are not appropriate for handling the vibrations and this may result in denting or brinelling of the bearing races.
Bearing Seals
This part is reacts very sensitively to the shaft radial movements. Thus the movements may cause the bearing seals to fail prematurely due to an increase in the damage of the shaft. It should be kept in mind that labyrinth seals have a very low tolerance.
Bolts
Vibrations may result in pump and motor hold down bolts to become loose.
Tolerance
Vibrations will also cause damage to wear ring clearance and impellar settings.
Causes of Vibrations in the Pump
By investigating the causes of vibrations in the pump, we will know how the main parts contribute to vibrations in the pump. Vibrations in the pump may be causes due to mechanical reason, hydraulic factors or other reasons which will be described later.
Mechanical Causes of Vibrations
Unbalanced Rotating Components. Damaged impellars and non centric shaft sleeves
Bent of wrapped Shaft
Misalignment of Pump and Driver
Piper Strain by Design or due to Thermal Growth
Because of the mass of the pump base, in case it is too small
Due to the thermal growth of various components, especially shafts
Rubbing Parts
Due to loose or worn bearings
Due to loose hold down bolts
Loose parts
When a product is attached to a rotating component
Damaged Parts
Hydraulic Causes of Vibrations
Operating off of the pumps BEF (Best Efficiency Point)
Due to product vaporization
Due to impellar vane running too close to the pump cutwater
Internal recirculation
When air is allowed to enter the system through vortexing etc
Because of turbulence in the system such as non-laminar flow
Because of water hammer
Apart from the mechanical and hydraulic causes, there can also be other causes of vibration such as
Harmonic vibrations from other nearby equipments may contribute to the vibration
Due to speed, when the pump is operated at a critical speed. This problem is especially common in pulley driven and variable pumps
Due to seal slip stick at seal faces, in case of pumping of non-lubricating fluid, a gas or a dry solid.
Vibration may also be caused a pump discharge recirculation line aimed at the seal forces
Chapter 2
Literature Review
The purpose of the literature review is to investigate the causes of vibrations in water pumps, how they arise and what methods can be used to control them.
According to R. Rayner, vibration may be caused by sources such as abnormal suction conditions, lack of proper lubrication, recirculation, when the pump is not properly designed, improper application of base plate and grouting procedures, lack of attention to coupling fitting, balance or key or when seals, fittings or flush cooling are improperly selected (Rayner, 1995, p. 203)
The above mentioned causes have been studied in detail in the literature of the report, However we will study them briefly here. Vibrations due to abnormal suction conditions usually because of dysfunction of the first stage impeller. Due to a deformity which will be studied in detail, this impeller starts absorbing vapor, and consequently the entire pump becomes vapor locked as the vapors not able to exit via the discharge valve. Thus the pump may become clogged and other damages also result.
Lack of lubrication is also a problem that is related to cavitation. The concept of cavitation will be studied in detail, but it is important to mention here that cavitation leads to vapor locking which inturn affects the capacity of the impeller to pump fluid. The bearings then becomes devoid of lubrication. This results in galling when they come into contact with the stationary parts. Cavitation can be avoided by ensuring that the Net Positive Suction Head Available, which displays the pressure in absolute terms at impellers eye, is always greater than what has been specified by the maker or the pump. (Haman, Izuno Smajstrla, 1989). NPSHa can be computed via the formula
NPSHA Barometreic Pressure Suction Head or Lift Friction Loss in the pipe Vapor Pressure ata given temperature (Haman et al., 1989)
We also know that the original seals and bearings is not able to handle vibrations effectively, therefore various modifications have also been proposed by various researchers. These modifications are designed to increase stiffness and damping capabilities. Since the center and throttle bushings were destabilizing, one method to increase the stability is to modify the seals especially the center bushings. When rotating rotor groves are removed, minimum clearance levels can be maintained for the entire length of the stationary bushing. This new annular seal when compared with the previous grooved seal has found to have more damping (50 more) and reduced cross coupled stiffness levels. Other readings involved logarithmic decimal values increasing to around 0.3 (we will compute later to show that positive log decimal values ensure stability of the rotor, while a value 0.3 log decimal should be maintained during normal running conditions) even at low aerodynamic loads, while the value still remained positive at even higher loads. When the performance of this pump with the modified rotor was compared with the other pump, it showed greater stability, thus it was recommended by the manufacturers that such modifications be done.
Chapter 3
Methods (Examining the Pump in Lab)
Previously we discussed the causes of vibration in water pumps and the adverse effects of vibrations on different mechanical components of the pump. Now we will attempt to explore how this vibration is caused, and which parts of the pump contribute to the vibration. Vibrations in centrifugal water pumps can be caused by both synchronous and non-synchronous ways. Synchronous ways of vibration include vane pass frequency energy and running speed energy, however vibrations due to non-synchronous ways result in more damage because of the inability to diagnose these issues due to the vagueness of exciting mechanisms which cause the vibrations. Non-synchronous ways of vibration include recirculation, stage hall and instabilities of the shaft.
Shaft
In machines, vibrations due to shaft may result when it is bent. In this case the shaft basically loses the power to rotate about its axis. The following experiment would help reveal the reasons for a bent shaft in a water pump and the associated vibrations which are caused. The reasons are basically attributed to upthrust forces which not only cause extensive vibrations but also result in bent shafts and vapor locking which affect seals and bearings. A series of tests can help demonstrate this effect, such as these field tests which were conducted on two pumps. The tests were conducted to obtain the following information
Flow rates
Parallel pump operation effects
How opening of the discharge valve affected the upthrust forces
The data was obtained with the aid of transducers, both fixed and temporarily incorporated transducers. The following data were obtained.
Suction Static and Dynamic Pressures
Both the static and dynamic pressures were recorded with the help of a transducer incorporated in the drain after upstream portion of the pump. A second transducer was incorporated inside the head of the pump. In this case the use of the transducer is similar to using a manometer which helps record the pressure at the pump section bell.
Discharge Static and Dynamic Pressures
In this case, the location of the transducer which will help measure the static pressure is just downstream of the pump at the location of the vent.
Pump Shaft Vibration
Installations of the proximity probes were done at the levels of mechanical seal and the bottom of the motor. The installation of these probes was done radially. The probes were installed in pairs, the two probes having a separation of 90 degrees from each other. These probes served two purposes, first it helped obtain the orbit of the shaft vibration and secondly shaft centerline positions could also be determined. To calculate whether the direction of the shaft impulsion is upstream or downstream, a third probe was installed which was positioned vertically to the other two probes.
Suction temperature in pump barrel
Heat temperatures in the pump barrel were calculated with the aid of a thermocouple which was incorporated in the drain of the pump barrel.
Vibration of Motor and Pump Housing
In order to measure vibrations of motor and pump housing, triaxal accelerometers were put on top of the motor and the head of the pump discharge. This helped in calculating the direction of the vibrations resulting from the structure.
Motor Current
Clampon amp probes were used for this purpose.
Flow Rates
The equipment which was installed in various portions of the pump helped calculate the monitor and calculate the flow rates.
Motor Speed
For this purpose an optical tach was used.
All the information which was obtained as a result of the field tests were recorded by using a 32-channel digital tape recorder. Other equipments which were used include a spectrum analyzer which was used for drawing spectrum plots. Time domain data were obtained from analog to digital convertor and proprietary software was used to control both the equipment and help in acquiring the data.
Pump 1 1st Start with Discharge Valve Fully Open
Discharge valve was kept fully open before starting this pump. Venting of the pump was also completed before the pump was started. This venting procedure is used to remove vapors and ensures that the liquid in the system is full. The bypass valve around the recycle valve was slightly opened after closing the recycle valve. Increasing the suction pressure in the pump can by 100 psi lifted the pump shaft vertically to about 20 mils. All this had happened before the pump had started operating. However, according to the producer of the pump, this behavior was not uncommon. It resulted mainly because the unbalanced force on the pump shaft was larger than pump rotors weight itself. Thus the motor was in an upthrust position when the pump had started.
Full speed was reached in 1.75 seconds. As with the case of the discharge pressure it showed a gradual increase and required a time of around 30 seconds to move to the point of 400 psi. No flow was thus indicated till 20 seconds after the start of the pump. A maximum flow rate of 1200 gpm was achieved after an interval of 30 seconds which resulted in the pump to trip. This flow rate seemed inappropriate since it was even higher than the maximum flow rate of the pump. It might be that this discrepancy had occurred due to vapor in the piping of the pump which resulted in an incorrect reading of the flowmeter
This upthrust condition was maintained for about 25 seconds and till the discharge pressure had increased to about 200 psi. It is this upthrust condition which can cause bending of the shaft, thus leading to vibrations in the pump. Thus it needs to be avoided.
Pump 1 2nd Start with Discharge Valve Fully Open
Before this pump was restarted again, the runout of the pump was measured by pressurizing the barrel of the pump. Thus it meant that the shaft was in the upthrust position. The runout had increased from 7.5 mils to about 12 mils. It was revealed that the bending of the shaft was just temporary which was caused by the shafts upthrust position.
It took a time of around 25 seconds for the pump to reach a pressure of 500 psi which showed that the discharge pressure increased only gradually. 850 gpm was the highest recorded flowrate. It might be that this was the actual flowrate. Data revealed that the flow rates were correct, since the current data of the motor was not constant. Also the motor amps were somewhat reduced during this period of high flow rate. An upthrust position was maintained by the shaft until the pressure reached above 200 psi. This position was maintained for about 15-20 seconds. As the discharge pressure increased above 200 psi, the vibration on the shaft started to decrease. This was because the downthrust of the pump increased with a higher discharge pressure. We know that when the shaft is in tension, the pump should operate in downthrust.
Pump1 Pump Startup with Slight Closed Discharge Valve
The previous tests helped to reach the conclusion that the startup of the pump should be done with a partially closed discharge valve. This will also help to achieve the required pressure in a shorter period of time, thus reducing vibration. It took the pump only 1.5 seconds to reach its full speed. The discharge pressure also reached 350 psi in just about 1 second. Because of the partially closed discharge valve only a period of 0.5 second was taken by the pump to change its position from upthrust to downthrust. With the discharge valve fully open this time period ranged from 15-25 seconds. The vibrations of the shaft were found to be greatly less when position of the pump was changed from upthrust to downthrust. Here the vibrations remained largely the same over a large flow range before the pump switched to a downthrust position.
Thus to reduce the shaft vibrations caused as a result of upthrust forces it was recommended that the pump should be started with an almost closed discharge valve. Gradually opening the valve after a few seconds of operation helped ensure that the pump operated with constant vibration levels.
Pump 2 Start with pump 1 running
This was a new pump with all parts being unused such as a new first stage impellar and Graphalloy Thus it contained new parts except for a few column bushings.
Before starting the pump, the shaft was rotated manually by hand and the runout which was measured at the mechanical seal was about 4 mils without any suction pressure. With 180 psi suction pressure this runout was increased to about 12 mils in the upthrust position. The increase was attributed to compression of the shaft in the upthrust state.
This pump was turned on while the 1st pump was already running. Since the first pump was already running, this pump was started with the discharge valve fully open. Downthrust position was achieved after 0.5 seconds of startup. The discharge pressure increased quickly as the pump achieved full speed. The vibration levels reduced form 9 mils to 4 mils after the downsthrust position was achieved.
After 9 seconds of start of the 2nd pump, the 1st pump tripped off. After tripping, the axial position of the 1st pump switch to upthrust as the discharge pressure was lessened to the level of suction pressure.
When this pump was turned off, level of vibration increased to about 11 mils during the coastdown when the upthrust position was reached. The vibration calculated in the upthrust position before the pump was started was the same as this shaft vibration. This indicated that the shaft had not bent during the operation.
Conclusion of the Tests
Using the measured data at hand, technical references and after evaluating the failed pumps, the following conclusions can be drawn
High shaft vibrations were produced when the pump was operated with discharge valve fully open. These high vibrations contributed towards bending the shaft. This resulted because the shaft operated with high vibration levels in the upthrust position for a period of 15-25 seconds.
When the discharge valve was fully closed, the shaft did not become permanently bent. This was because the upthrust position in this case was maintained for a period of only 0.5 seconds.
However when the pump was started with the discharge valve fully open while another pump was in service yielded good results. This was because of the pump was started against a high discharge pressure.
No record of cavitation was observed. This meant that vapors were not being produced in the pumps as a result of cavitation at the impellars.
The data from proximity probes revealed that at specific conditions the shaft was deflected radially. This resulted in the shaft being forced against the bushings. It is believed that this force against the bushings would increase when the shaft is bent. This increase in the force against the bushings due to bent shaft resulted in higher temperatures at the bushings. This heat can then result in the liquid to vaporize. In the absence of a vent system, this production of vapors could result in vapor lock at the impellars. Finally the pump could also fail as a result of lack of cooling.
When the field tests were conducted, the vent systems were also installed in the pumps. However, no increase in incidence of rising temperature levels was recorded. This showed that vapors were not being collected.
Vibrations increased to high levels as a result of the shutdown. This resulted because the shaft remained in the upthrust condition for a period of 25 seconds as the pump was coasting down. It is thus important to reduce shutdowns which could help prevent seal wear.
Shaft vibrations were greatly increased when the pump was allowed to operate in the upthrust condition. The prior failure of seals was also attributed to this fact.
Altering the startup procedures helped in eliminating such failures.
The field tests also revealed that only vibration levels at the shaft should be used as a standard to evaluate vertical pumps as compared to vibrations at the motor and pump discharge housing. This is because vibrations at these areas remained low even when the shaft vibrations were high.
Thus the field tests illustrated here how the upthrust forces contribute to the shaft being bent which inturn increases the vibration.
Bearings and Impellar
Vibration at bearings is the root cause of most vibration problems in mechanical devices. The problem usually starts here and later spreads to every part. The root cause of vibrations produced as a result of bearings and impellars in pumps is the phenomenon of cavitation. This process is explained as under
Because of low pressure, the volume of liquid may burst forming a cavity. When vapor gases start evaporating into the cavity from the vicinity, the cavity no longer remains a perfect vacuum but it has a perfectly low gas pressure. Thus due to this pressure difference (between the surrounding and the cavity), the bubble collapses. Temperature and pressure inside the bubble are elevated. A lot of energy is released as a result of this collapse as the gas inside the bubble spreads into the nearby liquid. At this point the temperature may reach up to several thousand Kelvin and the pressure may soar to several hundred atmospheres. Thus this whole process may result in destabilizing forces to act on the impellar and result in high vibrations of the rotor.
In pumps there are two form of cavitaion which are produced, discharge cavitation and suction cavitation. (Dowson Taylor 1979, p.35)
Suction cavitation is a low pressure high volume condition where the liquid first turn into a vapor. This vapor however is unable to discharge itself from the impellar because of the absence of vacuum. It is then converted back into the liquid. This can have great impact as it damages the face of the impellar. It may either have large chunks of material being removed from its face or small pieces. Thus impellar may end up having a sponge like appearance. In both mentioned cases the end result is premature impellar failure which will occur as a result of bearing failure. This form of cavitation can be identified with a gravel of marbel like sound emerging from the pump casing. The other form of cavitation (discharge cavitation) usually happens in instances when the pump is performing its operations at 10 of its BEP (Best Efficiency Point, for BEP calculation see page 35). Under these conditions, the discharge pressure is very high resulting in the fluid recirculation inside the pump as it is not able to exit the pump. As the liquid flows around the impeller, it must pass through the small clearance between the impeller and the pump housing at extremely high HYPERLINK httpen.wikipedia.orgwikiVelocity o Velocity velocity. This velocity causes a vacuum to develop at the housing wall (similar to what occurs in a HYPERLINK httpen.wikipedia.orgwikiVenturi_effect o Venturi effect venturi), which turns the liquid into a vapor. A pump that has been operating under these conditions shows premature wear of the impeller vane tips and the pump housing. In addition, due to the high pressure conditions, premature failure of the pumps mechanical seal and bearings can be expected. Under extreme conditions, this can break the impeller shaft. This form of cavitation can be identified with the sound similar to knuckles cracking.
As discussed earlier vapor locking of the impellars of the pump may also result in lack of lubrication at the bearings. This happens usually when the first stage impellars starts absorbing huge amounts of vapor. It results in small vapor bubbles passing through the impellers. This large amount of vapor can reduce the ability of the impellar to pump fluid. This starts a vicious cycle because the subsequent impellars also become vapor locked due to lack of flow of fluid into them. This process continues until the entire pump becomes vapor locked. Vapor locking can be avoided by continuously venting the pump barrel. Thus vibrations due to bearings are produced as a result of a disability of impellars to pump fluid because of whole process of cavitation. Without proper lubrication the bearing would gradually deteriorate and fail, but before the fault is detected, this results in the damage of other parts of the machine. Thus lack of lubrication at the carbon bushings produce heat which can result in the failure of these bushings. This can cause galling between the stainless steel parts because the wear rings on the impellars are now in direct contact with the stationary parts.
Chapter 4
We have demonstrated in our discussion the impact of upthrust forces that is how they contribute towards vibration which not only causes bent shaft but also cause damage to the seals and bearings. In specific cases, upthrust forces may also cause pump failure. Several solutions are therefore proposed to deal with the problems associated with these upthrust forces.
Hydraulic Analysis should be performed by the maker of the pump. This is necessary in case the running conditions such as flow rates, discharge and suction pressure are changed or fluid properties (such as specific gravity) vary significantly from the original values.
In a situation where the pump is running alone, it should be started with the discharge valve slightly closed. After the discharge pressure is fully developed after a few seconds this discharge valve can then be fully opened.
However in a situation where another pump is also running, the discharge valve can be kept fully open. The reason for this is that in this case the pump will be started against a high discharge pressure.
Effort should be made to lessen the number of startup and shutdown times. This is because of the upthrust conditions which exist for a short period of time during startup and shutdown of the pump. This effect has been demonstrated in the field tests which were discussed earlier.
In order to get an accurate picture of the extent of shaft vibrations proximity probes should be used instead of velocity transducers on the motor pump thrust stand. The latter is an ineffective way of measuring upthrust problems. Additional proximity probe could also be installed located axially to calculate upthrust.
Apart from upthrust forces, vapor locking which causes lack of lubrication at the bearings can also be reduced by creating proper venting mechanisms and certain design modifications.
To prevent vapor locking proper venting of the pump barrel is imperative at the auxiliary and seal components. Other than water pumps, this process is important in all the pumps, especially for liquids which are near the vapor pressure such as LPG because they evaporate quickly and hence can easily result in vapor locking.
Venting of the pump barrel should also be done continuously to the vapor side of the suction vessel with liberal size piping.
Apart from this above mentioned piping modification, other modifications which are proposed to reduce this instance of vapor locking. The purpose of these modifications is primarily to reduce cavitation which could inturn result in vapor locking. Cavitation basically means formation of vapor bubbles which occurs when the pressure of the liquid falls below the vapor pressure.
In order to lessen the Net Positive Suction Head Required (NPSHR), it was proposed that the diameter of the first impellar should be larger.
The original carbon bushings should be replaced with another Graphalloy nickel impregnated carbon bushings.
In order to prevent the pump from operating in a condition of low flow rates, an instrumental modification was proposed. This involved adding another instrument on the motor switch gear to enable the plant Distributed Control Systems to monitor the motor currents. Logic modification was added to the DCS which enabled the plant to trip in instance when the motor amps were operating below the minimum flow rates.
Another modification involved installing nickel bronze wear rings in place of the pumps stainless steel wear rings. Such a replacement would reduce the likelihood of galling.
Other modifications were proposed to reduce the impact of destabilizing forces at the rotor. These include
Air Injection
During the tests there was a perception that the cavity behind the impellar was serving as a bearing or a seal which were contributing to the destabilizing forces. These forces were very strong and caused the rotor to become unstable. Thus in an effort to lessen the effects of pressure forces in the cavity behind the impellar, tests were conducted. The tests involved allowing air to enter into the cavity which immediately put an end to the vibration. The idea was to decouple the fluid from the rear end of the impeller shroud. This helped in ending the rotating pressure field.
Despite the usefulness of this method to terminate the vibration, it was not considered feasible due to certain operational restrictions.
Increasing the Wear Ring Clearance
In this technique the pump was elevated to establish if the instability vibration would be affected as a result of the increase in clearance between the impellar and the wear ring. This also helped end any consequence of the wear ring and the impeller rubbing together. These proposed changes when put into affect did not yield favorable results. At supersynchronic frequencies, the increase in the ring clearance had no affect on the amplitudes of vibration.
Stationary Spoilers
The purpose here was to try to break the rotating pressure field at the back of the impellar. For this purpose spoilers or 8 small stationary ribs were incorporated on the pump case. This whole process was done without dismantling the pump. The spoilers were just fixed to the housing. Spoilers were limited to a height of about 38 inches because of space issues. Data which was obtained at the spoilers showed that the backward mode vibrations were attenuated. The point of differential pressure where the instability happened was increased it was increased from 19-25 feet. The fluctuating levels at the backward state were still large. Thus it was believed that by raising the height of the spoilers or increasing the number which are installed, effectiveness of the spoilers may be increased to cope with the destabilizing forces.
Prior experiments revealed that when clearances at the back of housing and the impellar shroud are reduced, the pressure created by the impellar rises sharply. These tests were performed with a spacer with 24 radial grooves. These grooves had direct affect of lessening the tangential speed in the leakage annulus, thus reducing the cross coupling hardness in the same manner as the stator roughness in a damper seal. The tangential velocity was also reduced, in the same way as in the grooves. Thus this process had the effect of reducing the impact of destabilizing forces.
Expeller Vanes
This process involved implanting of the small vanes at the rear end of the impellar. The purpose here was the same as in above experiments such as to reduce the impacts of destabilizing forces on the rotor. The expeller vanes could serve here to reduce the pressure difference formed across this impellars rear end, thus helping to lessen these destabilizing forces.
Space restricting led to dismantling the pump, without which this installation process would not have been possible. The space restrictions also restricted the height of the installed vanes, because of the clearances. Thus specially formulated vanes were developed for attachment to the impellar shroud. Data collected after this attachment of the vanes revealed that the instability vibrations were eliminated. Thus the solution for the problem of the destabilizing forces was established. This discovery was made an unchanging modification. There was some concern about the loosening of the bolts which were used to fix the vanes, however no such problem has yet arisen and functioning of the pumps seem to be smooth.
Chapter 4
Results
Calculations
Allowable Vibration Levels
Allowable levels of vibrations for vertical pumps have been prescribed by API Standard 610 (1995). The allowed vibration levels on the pump thrust bearing housing are 0.2 in per second root mean square (rms) and 0.3 in per second zero per peak. The following equation is used in calculation of these allowable vibration levels.
A 10,000 N
Au unfiltered displacement determined by the Fast Fourier Transform (FFT), mils peak to peak (not e 4.0)
N root mean square
We can approximate the allowable vibration levels with the help of this equation to equal 2.4 mils peak-to-peak at 1795 rpm and 1.7 mils peak-to-peak at 3570 rpm.
Calculating Net Thrust Forces
The net thrust forces are due to the both upward and downward forces which are acting on the pump
The downward forces emerge as a result of unbalanced pressure forces as well as because of the weight of existing parts
Upward forces emerge as a result of flow through the impellars caused by a change in momentum.
A simplified model will be presented here to determine these forces. However this model can be altered depending on the type of pump and its working.
Downthrust Force
Downthrust forces result because of unbalanced forces across the impellar. Suction pressure acts on upper and lower impellar shroud and discharge pressure acts on the impellar eye. By using the equation formed by Dufour and Nelson in 1993, these downthrust forces can be calculated. It has been observed that the highest downthrust level exists at the pumps shutoff position due to the higher head of the pump.
Fd ((constant)(H)(SG)) Rotor Wt
Fd Downthrust, lb
H Head, ft
Constant (Net eye area)2.31, lbft
SG Specific Gravity
Rotor Wt Total weight of shaft and impellars in lb
Upthrust Forces
The fluid passing through the impellar can produce the upthrust force because of the change in its momentum. By calculating the kinetic energy, V (2g), of fluid, these upward forces can be determined. As the velocity of this fluid which flows through the impellar increases, the upthrust forces also increase. This is why we see that these upthrust forces become really high as flow rates increase to high levels.
The following equation is used for calculating upthrust forces in case of fully radial flow. Upthrust forces in mixed flow impellars can be computed by multiplying the following equation with a value between 0 and 1, depending on the extent to which flow becomes radial. Axial flow impellars do not result in upthrust forces.
Fu 1 c ( Ve 2g) Ae
Fu Upthrust, lb (N)
Ve velocity in impellar eye, ftsec (msec)
g 32.2 ft sec (9.81m sec)
c Unit Conversion Constant, 2.31 for USCS, 1.02 for SI
Ae net eye area in cm
Calculations for Computing Axial Forces with the Help of Impellar Thrust Factors
Usually a hydraulic constant is provided by K for each impellar type which is the Hydraulic Thrust Factor. BEP that is operation at Best Efficiency Point is used to compute K. Best Efficiency Point can be calculated as follows
E whp bhp x 100, here
whp water horsepower
bhp break horsepower
However this method does not provide an exact value, because upthrust forces vary with the capacity. This component is unable to account for such factors. Thus thrust-capacity curves are usually used by the pump manufacturers to compute the impellar thrust. For example,
K is read from the curve and given root mean square value. K value attributes both upthrust and downthrust forces.
Then K (total pump head times specific gravity of liquid)
Discharge pressure should be lessened above the impellar eye with the help of balancing holes and rings in case the impellar thrust is very high, thus hydraulically balancing the pump. This helps in lessening the K value.
Increasing Shaft Stability by Using Pumpout Vanes
In this part computations show measurements which were done for the solution of super synchronous shaft vibration problems in centrifugal water pumps. At low discharge pressures, centrifugal water pumps were marginally stable however they became unstable as the pressure increased. As discussed earlier pumpout vanes were incorporated on the back end of the impellars to solve the vibration problem. These vanes were incorporated in a two stage centrifugal slurry pump. This pump was a installed as a coke crusher pump in the refinery. It had unshrouded (open) impellars. The performance data of the pump are shown as shown
Excessive shaft vibrations were experienced by the pump during shop acceptance tests of the pumps operation in water. This high level of vibration also resulted in contact of the pump with other stationary parts, particularly the centre bushing and the inward bearing housing seal. It was observed that the shaft frequency was 1.3 running speed, that is 4800 cpm while the pump was operating at 3600 rpm. Such vibration level was not routine.
Impact Testing To Measure the Rotor
Mechanical Natural Frequencies
Dry rotor natural frequencies were measured with the help of impact tests. The purpose was to determine the cause of vibration at 1.3 running speed. The rotor was mounted on the balance stand after being removed from the case. A significant response was indicated via the impact test at around 1.5 times the running speed. This was brought about by impacting one of the impellars parallel to the shaft. It was determined via the computer analysis that the response near 1.5 times running speed was not a natural frequency of the impellar but a natural frequency of the pump rotor.
Effect of Added Stiffener Vanes
Since it was believed that the previously measured effect was the result of high vibration, five stiffener wanes were incorporated to the rear side of the impellar in an attempt to raise the mechanical natural frequency of the impellar more above the running speed. Subsequent testing with the incorporated vanes revealed that vibration levels were eliminated which were present before 1.3 running speed. New modified impellars were developed, after the previously encouraging results. These had the same stiffner vanes as before but a thicker back plate. This did not yield fruitful results and the vibration elevls again became high at 1.3 running speed. Tests were again performed with the previously incorporated five stiffener vanes, which again showed that vibration levels were non-existent 1.3 running speed.
It was believed that the stiffener vanes helped lessen the pressure drop across the centre bushing and it is thought that they may have also reduced the aerodynamic loading on the impellar blades. Thus the stiffener vanes worked similar to pumpout vanes. It was however not possible to establish the difference between these impellar vanes and the modified version which was incorporated later with a thicker back plate. However it was believed that the difference could be attributed to welding of vanes to the rear end of the impellar. When the vanes were incorporated first, a sharp angle was formed between the vane and the impellar. The modified impellars had full bead welds on sides of the vane resulting in a smooth fillet on each side. Thus due to the advantage of the sharp angle which the original vanes had, they may have been more effective as pumpout vanes.
Stability Analysis
It was determined that the vibrations which were being caused at 1.3 running speed were due to rotor instability problem. There was a need to determine whether the vibrations were being caused by self excited mechanism or if it was the result of high pulsation forces. Proximity probes and piezoelectric dynamic pressure transducers were used for this purpose. Shaft vibrations were measured with the help of proximity probes and pulsation was measured with pressure transducers. Piezoelectric dynamic transducers were incorporated in the pressure tap areas in the suction and discharge piping and to centre of bushings and throat bushings in the seal flush lines.
The data which was obtained revealed that the pump became unstable as full speed was reached and the discharge pressure was raised. According to the data at specific running conditions, which were away from the Best Efficiency Point (high pressure, low flow low pressure, high flow), the rotor became unstable and circled in the forward direction. Frequency analysis showed that instability frequency near 1.3 running speed resulted in increased vibration levels. Vibration was also increased as the pump operated away from BEP. At the center bushing, the pulsation data correlated with the shaft instability vibration. It was difficult to determine at that time whether the vibration was being caused by pulsation or if pulsation was being caused by vibration at instability frequency. However later it was established that vibrations at 1.3 running speed were occurring as a result of self excited rotor stability. This meant that at the instability frequency pulsation was the result, rather than the cause of shaft vibration.
In self excited rotor dynamic instabilities, the rotor will circle at a frequency which is near a rotor lateral natural frequency. The instability vibrations will be subsynchronous (less than the running speed) in case the rotors function above the first lateral natural frequency. It will supersynchronous (above the running speed) in case the rotors function below the first lateral natural frequency.
These self excited instability vibration levels can increase further until they are limited by some non-linear effect, or until a rotor is able to contact some other part such as seals or center bushings. Differential loading on the pump impellar blades were supplying the energy for the instability vibrations. The pump is impelled to circle in the direction of the rotation because of this differential loading on the blades which creates cross coupling forces. Thus Kxy, which are known as cross coupling stiffness coefficients are produced by these cross coupling forces. The formula used to calculate these coefficients are shown below, which was later altered for use with centrifugal compressors.
Kyx -6300 (HP) (MW) N d h x ds
HP horse power
MW molecular weight
d discharge density
s suction density
N speed, root mean square
D impellar diameter
h minimum restrictive dimension in flow path
This equation will be modified for our use and application in centrifugal pumps. The term aerodynamic loading will be used in this case, even though we are not dealing with gas here. This is because originally the forces were applied to turbines and compressors where the loading was termed as aerodynamic loading. Thus to compute the aerodynamic cross coupling can be estimated as follows
Kyx -6300 (HP) N D h
Basic Concept of Rotor Stability
We can think of instability as a free vibration of a system having a negative damping.
Free vibrations disappear in a system of positive damping as soon as the exciting force is removed. However in a negative damping system when the vibration is initiated by such disturbance it grows without being limited.
Mathematically, instability can be shown as
mx cx kx0
This is called the differential equation of motion, here
k stiffness
c damping constant
m mass
x displacement
The solution for this formula is
x e-(c2m)t eiwt
or x e-(c2m)t (A cos t B sin t)
When amplitudes of vibration x1 and x2 occurring n cycles at times tt and t2 are compared, the dampening systems can be analyzed. Thus the above ratio is reduced to
x2 x1 e-(c2m)t
However if the quantity
e-(c2m)t 1
Then the vibrations will increase with the time as shown above
Therefore if ct2m 0, then the vibrations will be unstable. We define c2m as , the growth factor.
The logarithmic decrement (log dec) is defined as
c2mn , for small , then
2pi, therefore the log dec can be written as
2p -2pi n -f
The above is a convenient form of logarithmic decrement relationship as the eigen values for the damped critical speeds have the following form
s i, here
whirl frequency
growth factor, 1sec
Because here is positive, log decrement for a stable vibration (0) will also be positive. We see that theoretically rotors which have a positive log decrement value are stable. But under normal running conditions, logarithmic decrement should be about 0.3 for the entire rotor with the impact of the seal established at full load condition (full aerodynamic loading). This will help make sure that the rotor is stable under such conditions. For logarithmic decrement values between 0 and 0.3, the rotor is considered as marginally stable.
Rotor Stability Analysis
A computer program which used Myklestad-Prohl process was used for the stability analysis. Dampened eigen values and growth factors were computed.
We have mentioned in the literature review above of the modifications in the bearing to increase stability and the accompany increase in log decimal values that result. The following tables show the comparison of performance when the grooved seals were replaced by annular seals (Smith, D.R, Price, S.M. Kunz, F.K)
Table SEQ Table ARABIC 2 Comparison between Grooved Seals and Annular Seal Performance
Kxx (lb ftin)Kxy (lb ftin)Cxx (lb f-sin)Cxy (lb f-sin)Mxx (lb m)Grooved Seal PerformanceCenter Bushing (H2O)10,50011,60013.01.21.5Center Busing (HC)8,6009,60011.51.61.5Throttle Bushing (H2O)6,1003,4007.80.70.6Throttle Bushing (HC)4,8002,7007.30.50.6
Kxx (lb ftin)Kxy (lb ftin)Cxx (lb f-sin)Cxy (lb f-sin)Mxx (lb m)Annular Seal PerformanceSmooth Center Bushing (H2O)22,5006,00019.50.70.5Smooth Center Busing (HC)19700590019.40.60.4Smooth Throttle Bushing (H2O)8,5002,00010.80.20.2Smooth Throttle Bushing (HC)6,400 2,00010.80.20.2Source Adopted from Smith, D.R, Price, S.M. Kunz, F.K, viewed December 27, 2009 www.engdyn.compapersabstractsab75.htm
We see now that rotor instabilities were the cause of supersynchronous vibrations. Also because of little damping which was given by the anti friction bearings, the rotors were marginally stable. Cavities were responsible for producing the destabilizing forces which resulted in the vibrations. These cavities were formed between the impellars and the pump housing. Both backward and forward instability rotor vibrations were generated by these forces. Two theories have been formed to account for this instability, since it remains uncertain if pulsation (inside cavities at the back of impellars) caused vibration or if it was the other way around.
Theory 1 Because of the pressure wave which forms in this cavity, an impellar is provided with a force and thus causes rotor to vibrate. Various methods have been discussed above to reduced the impact of this instability such as with pumpout vanes by lessening the pressure in the area, with spoilers by lessening the tangential velocity of the fluid or with the help of air injection. The aim is to reduce the pulsation waves that will inturn aid in lessening of rotor instability.
The theory has some weaknesses. Firstly it does not account for why the pulsation was formed in the first place inside the cavity. Secondly it also does not help explain why the pulsation spread forward and backward.
Theory 2 Cross coupling forces on the impellar may be generated by cavities at the back of pump impellars when they act as seal or bearings. The extent of the force is determined by the dimensions of the cavity which impact clearances amid housing and impellar. All techniques described above such as spoilers, pumpout vanes and air injection helps in lessening the cross coupling forces, thereby directly subsiding the rotor instability. Pumpout vanes also aid in the reduction of the differential pressure across the cavity, this further helps in the diminishing process. A similar effect can be achieved by lessening differential pressure across the seal. The analytical support to such theories cannot be computed, since the current techniques are insufficient to examine characteristics of cross coupling forces in the ring cavity.
It is not necessary for a direct contact between rotating and stationary components to occur for backward rotor instabilities. Destabilizing pressure forces at the rear end were enough to produce backward and forward shaft instabilities.
For both horizontal and vertical pumps, the stability of the shaft can be established by using the stiffness and damping coefficients (for both bearings and seals). Horizontal and vertical pumps were receptive of pressure forces at the back of impellars (since they had low logarithmic decimal value).
Quoted stiffness for the bearing alone is greater than the actual effective bearing stiffness for antifriction bearings. The effective bearing stiffness since bearing is supported by the combine stiffness of the bearing housing and the pedestal.
We can see that the rotor may circle at subsynchronous and supersynchronous frequencies, since the centrifugal pump rotors are sensitive to the destabilizing effects of seals. According to the analysis stability of smooth seals is greater than grooved seals. When the grooves on the rotating seals were lessened, the destabilizing cross coupling stiffness (Kyx and Kxy) was reduced and direct damping coefficients (Cxx and Cyy) was increased. Thus not only the rotor stability was increased but also the effective stiffness of the shaft was increased.
Antifriction bearings help lessen the damping values in comparison with journal bearings. Destabilizing forces which impact on the rotor result in both subsynchronous and supersynchronous vibrations. Various methods have been proposed to manage this instability. This can be done by either increasing the rotor stability or reducing destabilizing forces. Various methods have therefore been proposed which have been discussed above such as with the help of pumpout vanes, stationary spoilers and air injection.
Apart from the destabilizing forces which affect the rotor stability, upthrust forces also contribute to the vibration in pumps, cause bend shafts and sealsbearings damage. A direct link exists between the position of the discharge valve and the impact of these upthrust forces. Various methods have therefore been proposed when operating the pump o avoid the effect of such forces which contribute towards vibration. A hydraulic analysis should be performed by the pump manufacturer. Also when a single pump is operating, the discharge valve should be kept partially closed which can be opened after a few seconds of operation when the discharge pressure has been fully developed. In case of parallel operation with another pump, discharge valve should be kept fully open as it will be started against a discharge pressure in this case. Reducing the number of startups and shutdown will help minimize these forces as test has indicated upthrust conditions occur during this period. Proximity probes should be used for calculating shaft vibrations as shaft vibrations are difficult to detect with other forms and equipment.
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