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We were contacted by a leading South American petrochemical facility that had been beleaguered by persistent malfunctions of process machinery.  The machinery, large vibrating screeners, had been installed at the plant several years ago.  The malfunctions were caused by cracks that occurred along the welds, plates, and beams which comprised the structure of each screener, and occasionally by failures of the suspension cables that supported the screeners.  These structural failures rendered the vibrating screeners inoperable, and resulted in lost production of approximately 25 metric Tons/hour per screener.  With eight of these massive screeners operating within the facility, and at a salable product cost of $200/ton, the net production losses approached $1 million per day.  In addition, the recurring maintenance costs borne by the petrochemical facility were substantial.

The eight screeners were used in the synthetic production of urea from hydrocarbons.  Today the primary global demand for urea is as a nitrogen-rich solid fertilizer, but other applications include the manufacture of adhesives and polymers.  Near the end of the production process, each vibrating screener was fed a supply of urea pellets through top nozzles that were located near the gearbox end of the sloped hopper of the screener, see Figure 1.  The screener was driven by a constant speed induction motor through a gearbox.  During operation, an eccentric output shaft on the gearbox of the screener caused the hopper to reciprocate vigorously in the horizontal plane.  Mesh screens that were arranged within the shaking hopper enabled the pellets to be graded by size, and the sorted pellets then were discharged from the bottom of the screener.  The screener was supported with a fabricated base structure in conjunction with four suspension cables, also Figure 1, to accommodate the motion that occurred during its operation. 

Testing


Detailed investigations of two of the eight vibrating screeners were performed at the facility to identify the root cause of the screener failures, and to reach an effective, practical solution to the machinery problem for the customer.  While the screeners operated in the typical manner, a multiple channel spectrum analyzer was used to record detailed vibration data from the main structural components of the screener, which included the hopper and the base structure.  Operating Deflected Shapes (ODS) of the screener were created from this data to visualize the motion of the screener accurately during its normal manner of operation.  A modal impact test of one of the screeners also was conducted to establish the natural frequencies of vibration and the mode shapes of the screener assembly.  Because compliant connections facilitated relative motion between the hopper and the support structure, separate sets of impacts were performed on the hopper and on the support structure of the screener.  The hopper and the support structure were impacted both horizontally and longitudinally, and the responses were recorded at locations throughout the screener using accelerometers.  The representative vibration spectrum of the screener is shown in Figure 2, and the running speed and its harmonics are identified as peaks throughout the frequency spectrum. 

In addition, key dimensions of the screener’s structure that included the thicknesses of the plates and beam flanges were measured by the customer, to identify any potential deviations from the original design which may have been introduced inadvertently during the fabrication process.  All of the measured dimensions were confirmed to have been within the tolerance limits of the dimensions which had been specified on the engineering drawings of the vibrating screener. 

Analysis


Simultaneously, a three dimensional (3D) finite element model of the screener, which included the base structure, was created.  Drawings of the screener were supplied by the customer, from which 3D solid geometry models were produced (Figure 1) using the Pro/Engineer solid modeling software package.  The 3D solid model geometry was translated into the ANSYS finite element analysis (FEA) software environment, where it was distilled into a mesh of elements that represented the mechanical structure of the screener.  The appropriate element properties, material properties, and boundary conditions were assigned to the elements in order to create the comprehensive finite element model of the vibrating screener. 


vibe_fig_1

The 3D finite element model of the screener was used to conduct a detailed modal analysis that accounted for gravitational acceleration in the vertical direction, along with lateral and longitudinal accelerations which simulated the motion that was induced by the gearbox.  The finite element modal analysis predicted the natural frequencies of vibration and the associated vibration mode shapes of the screener.  The screener had been designed to segregate pelletized solid material, by size, through the application of periodic motion to the structure.  Therefore, the greatest vibration amplitudes occurred at the gearbox output running speed, i.e. 3.56 Hz or 1x running speed (Figure 2), and the bending or twisting modes beyond this rigid body motion were considered in the evaluation of the screener. 

vibe_fig_2

Diagnosis


The mode shapes that had been predicted analytically through the FEA were compared with the ODS model, which represented the experimentally-identified mode shapes of the screener.  For both the hopper and the base structure, the analytically predicted vibration modes occurred at frequencies that were approximately 1.5 times greater than the vibration modes which had been identified experimentally.  The results of the comprehensive modal evaluation indicated that the structural stiffness of the screeners which had been tested at the facility had diminished significantly, to a magnitude that fell well below the analytically predicted stiffness of the nominal design of the vibrating screener. 

Using standard equations for the vibration of flat plates, the welded plates that formed the structure of the screener were analyzed to gauge the influence of the edge boundary conditions on the plates’ natural frequencies of vibration.  Modeling the edges of the plates as clamped boundaries resulted in plate vibration frequencies that matched the FEA model’s predictions closely.  Modeling the edges as simply-supported boundaries resulted in plate vibration frequencies that fell consistently below those of the experimental modal data.  This outcome indicated that the edges of the plates, where the welds were located, had developed increased flexibility over the time which had elapsed since the screeners had been installed at the plant.  The response of each plate was characterized by a stiffness that was bounded by those of the simply supported and of the fully clamped edge conditions.  Micro-cracks, which had developed gradually in the welded joints, would cause a partial loss of the edge stiffness of each plate, an explanation that was consistent with the findings of the investigation. 

The vibration of the plates that made up the screener’s structure was found to have had an amplifying effect on most of the vibration modes of the screener, which occurred beyond 4.99 Hz.  This was most pronounced at the modes that coincided with the harmonics of the screener’s running speed, 3.56 Hz.  The plate modes that coincided with the running speed (lower harmonics) and with the first harmonic of the motor speed, 19.16 Hz, proved to be detrimental to the welds throughout the structure of the vibrating screener.  Excited by the resonances, the plates responded with enough energy to cause fatigue cracks to develop gradually in the welded zones of the structure.  Further, the bending and twisting which occurred during the resonant natural frequency modes of the hopper and the base structure generated a large amount of tension oscillation in the support cables.  This action promoted fatigue and the eventual failure of some of the cables to take place. 

In addition, a quasi-static finite element stress analysis was conducted to predict the steady-state operating response of the screener’s structure while it was loaded by the transient mass of the pelletized solid product.  The customer had supplied the approximate pellet loads that typically occurred at key portions of the structure during the operation of the screener.  Within the finite element model of the screener, the pellet loads were simulated and a quasi-static FEA was performed to predict the response of the structure to the loads.  The results of the FEA indicated that the transient mass caused relatively low stresses to occur at the key locations of the structure, which included the support lugs and the coupling between the gearbox and the hopper’s main header. 

Also considered was the worst-case net impact loading that was created by the loss of momentum that occurred as the pelletized product fell into the hopper of the screener.  Calculations showed that when integrated over the entire hopper, the net magnitude of only the pellet impacts would exceed the steady-state gravity load of the filled hopper if the average impact duration was less than one millisecond.  In view of the low modulus of elasticity of the product, the loss of momentum would require more than one millisecond.  Therefore, the rate of momentum transfer of the pellets would not create excessive forces on the plates of the hopper. 

These additional analytical findings implied that the sympathetic resonances between the lower frequency modes and the harmonics of running speed created the high stresses in the structure, and not the steady loads that were produced as the pelletized product was being processed.  Therefore, the excessive mechanical stresses in the vibrating structure of the screener caused the cracks in the welds to develop over time. 

Solution


To solve the problem of the failing vibrating screeners, it was recommended that any existing cracks in the main welded joints of the structure should be repaired immediately, both to restore the overall structural stiffness of the screener to approximately that of the theoretical design, and to prevent additional potential failures from occurring that would have been caused by the weakened joints. 

In addition, damping of the plate modes of the structure was recommended to reduce the amplification factor, and hence, the detrimental vibration response of the screener.  This was implemented in a practical manner by the application of commercially available constrained-layer damping material to the panels of the screener’s hopper (Figure 3). 

vibe_fig_3

To improve the service life of the structural beams and the support cables, it was recommended that the twisting and bending mode frequencies of the screener should be increased, to shift them further away from the driving frequencies of the vibrating screener and their harmonics.  The welding of strategically-located horizontal ribs along the main beams of the screener’s structure was suggested as the most effective means to implement this enhancement of the screener’s structural stiffness (Figure 4).  The reinstallation of the aluminum lid of the hopper with a thinner than was originally supplied rubber gasket, the addition of support bolts to the corners of the lid, and the retightening of the lid’s hold-down clamps were practical supplementary steps that also were suggested to shift the vibration frequencies of the screener upward. 

vibe_fig_4

Once implemented, these key modifications increased the operational life of the vibrating screener dramatically by eliminating the frequent failures of the structural beams, plates, and hanger cables which had made the screeners at the plant unreliable.  This action eliminated the large production losses that had beset the petrochemical facility, which contributed immediately to the facility’s profitability. 

Maki Onari, Manager of Turbomachinery Testing, supervises and performs Mechanical Solutions, Inc’s on-site rotating machinery testing projects.  Proficient in all of MSI’s analysis and testing tools, he has also conducted and directed a variety of finite element analysis projects.  His professional career of over thirteen years includes diverse petrochemical experience, and he has performed rotating machinery analysis, diagnosis, troubleshooting, and failure studies on steam turbines, gas turbines, centrifugal compressors, pumps, generators, motors, centrifugal dryers, and fans.  Through these efforts he has acquired significant test-stand and field evaluation know-how, and he also has participated in vendor selection/coordination, machinery specification preparation, witness acceptance tests, and machinery commissioning.  Maki possesses hands-on experience in the assembly, disassembly, installation, and maintenance of large machines.  He is a member of ASME and the ISO TC108/S2 Standards Committee for Machinery Vibration, and has lectured at the Texas A&M Symposia.

Eric Olson, Principal Engineer with Mechanical Solutions, Inc, is a recognized leader in the turbomachinery industry with over 25 years of experience, and functions in both technical and business development capacities at MSI.  His extensive background includes the design and analysis of centrifugal pumps and compressors, gas and steam turbines, and air dynamometers for the evaluation of turboshaft gas turbines.  He also possesses hands-on field engineering experience with high-performance engineered pumps and other rotating machinery.  In prior positions Eric and his staff established a turbomachinery design and development business, and he was a Regional Manager with the responsibility for all parts, repairs, and revamps of large industrial pumps in the western half of North America.  A multi-year short course speaker at the Texas A&M International Pump Symposium, Eric is a member of ASME, AIAA and, the Vibration Institute, and he is a Standards Partner with the Hydraulic Institute.  Mr. Olson’s current areas of focus include turbomachinery troubleshooting, turbomachinery design and analysis, and alternative energy.

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