Process Engineering Equipment Handbook 2009 Part 7 pdf

C-322 Condition Monitoring; Condition-Monitoring System(s); Engine Condition Monitoring; Engine Condition–Monitoring System(s) FIG. C-348 Critical speed map. 13 then w n <w nt Therefore, we see that flexibility lowers the natural frequency of a system. This is diagrammatically represented in Fig. C-348, which can be extended to include 2nd, 3rd, and higher critical speeds. Figure C-349A shows vibration modes of a uniform flexible shaft supported at both ends by rigid supports. Figure C-349B shows a rigid rotor supported by flexible supports. The critical speed concept theory outlines the identification of the operating range of a rotor-bearing system, probable mode shapes, and approximate locations of peak amplitudes. Forced vibration. In forced vibration the usual driving force in rotating machinery is the shaft speed or multiples of this speed. Note the characteristics of forced and self-excited vibration in Table C-29. The speed becomes critical when excitation frequency is equal to one of the natural frequencies of the vibration. In forced vibration the system is a function of frequencies that can be multiples of rotor speed excited by frequencies other than 1¥ rpm. They might be blade- passing frequency, gear-teeth frequency, and so forth. For forced vibration, critical frequency remains the same for any shaft speed. Damping reduces the amplitude of forced vibration but does not change critical speed values. Campbell diagram. Figure C-350 is a representation of a Campbell diagram. The Campbell diagram is an overall view of all the vibration excitations that can occur on an operating system. The numbered lines (numbers with a circle around them) are engine order lines. For illustration purposes, the second stage compressor blade has been theoretically represented. We see that operating the compressor at a specific speed range—12,000 rpm—will excite the 200-Hz first harmonic (200 Hz = 200 ¥ 60 = 1200 rpm). This range should be avoided. Condition Monitoring; Condition-Monitoring System(s); Engine Condition Monitoring; Engine Condition–Monitoring System(s) C-323 FIG. C-349A Rigid supports and a flexible rotor. 13 FIG. C-349B Flexible supports and rigid rotors. 13 TABLE C-29 Characteristics of Forced and Self-Excited Vibration 13 Forced or Self-excited or Resonant Vibration Instability Vibration Frequency/rpm N F = N rpm or N or Constant and relatively relationship rational fraction independent of rotating speed Amplitude/rpm Peak in narrow bands Blossoming at onset and continues relationship of rpm to increase with increasing rpm Influence of damping Additional damping Additional damping may defer to Reduce amplitude a higher rpm No change in rpm at Will not materially which it occurs affect amplitude System geometry Lack of axial symmetry Independent of symmetry External forces Small deflection to an axisymmetric system Amplitude will self-propogate Vibration frequency At or near shaft Same critical or natural frequency Avoidance Critical frequency above Operating rpm below onset running speed Axisymmetric Eliminates instability Damping Introduce damping To ensure that blade stress levels are within fatigue life requirements, one might strain gauge the blading on prototype test models to measure stress levels. An impeller might also be mounted on a shaker table with variable frequency output (0–10,000 Hz). Accelerometers can be mounted at various positions on the impeller and used with a spectrum analyzer to record frequency response. See Figs. C-351 and C-352. The results of all these tests may be plotted on a Campbell diagram, such as Fig. C-353. Lines of excitation frequency are vertical lines on the diagram. The design speed is represented by a horizontal line. When lines of excitation frequencies and multiples of running speed intersect near the line of design running speed, there may be a problem. C-324 Condition Monitoring; Condition-Monitoring System(s); Engine Condition Monitoring; Engine Condition–Monitoring System(s) FIG. C-350 Campbell diagram. 13 In the case, for instance, of an impeller with 20 blades, a design speed of 3000 rpm (or 50 Hz), and a critical frequency of 1000 Hz, the impeller may have a serious problem at these conditions (the intersection of the running speed line, 1000-Hz frequency line, and line of slope 20 N) as its critical is 20 N. Introduction to balancing using influence coefficients The theory of balancing using influence coefficients will not be dealt with fully here as it involves some cumbersome mathematics. However, this technique Condition Monitoring; Condition-Monitoring System(s); Engine Condition Monitoring; Engine Condition–Monitoring System(s) C-325 FIG. C-351 Accelerometer locations on impeller tested. 13 FIG. C-352 Impeller showing nodal points. 13 C-326 Condition Monitoring; Condition-Monitoring System(s); Engine Condition Monitoring; Engine Condition–Monitoring System(s) FIG. C-353 Campbell diagram of tested impeller. 13 is incorporated into modern multiplane balancing machines today. The accuracy of these machines is possible because of advances in sensor technology and minicomputers. Consider a rotor with n discs. Let P, P, ,P n be the forces acting on the shaft. Then the deflection Z i in the ith plane is given by: This equation defines the compliance matrix [e ij ] and the elements of the matrix are called influence coefficients. The compliance matrix is obtained by making P j =d y where d y is the Kronecker delta, and measuring deflections and Z j . As j is varied from 1 to n, each column of the compliance matrix is developed. Knowing the initial vibration in each plane q i , the system of equations is solved for the correction forces. The correction weights can be computed from the correction forces. In balancing with influence coefficients: ᭿ Initial unbalance amplitudes and phases are recorded ᭿ Trial weights are inserted sequentially at selected locations along the rotor ᭿ Resultant amplitudes and phases are measured at convenient locations ᭿ Required corrective weights are computed and added to the system This method requires no foreknowledge of the system dynamic response characteristics. If it were available it would help in selecting more effective readout locations and trial weights. Influence coefficients examine relative displacement rather than absolute displacements. Damping or initially bent rotors do not affect the process. Introduction to modal balancing The modal balance technique will not be discussed in detail in this course. It does, however, involve equating the deflection of a rotor at any speed to the sum of various modal deflections multiplied by constants that depend on speed. So a rotor that has been balanced at all critical speeds will then be balanced at all other speeds. The basic procedure for a rotor with end bearings is to first balance the shaft as a rigid body, then balance for all critical speeds in the operating range, then balance out any noncritical modes at the running speed. Typical principal modes (1st, 2nd, and 3rd) for a symmetric and uniform shaft are illustrated in Fig. C-354. Modal balancing, mathematically speaking, is based on the fact that a flexible rotor may be balanced by eliminating the effect of the unbalance distribution in a mode-by-mode sequence. The deflections of a rotor at any speed may be represented by the sum of various modal deflections multiplied by constants dependent on speed. where represents the amplitude of transverse vibrations, as a function of the distance along the shaft at a rotational speed w. and h r (x) express the complex coefficient at rotating speed w and the rth principal mode, respectively. In other words a rotor that is balanced at all critical speeds is also balanced at any other speed. For end bearing rotors, the usual procedure is: B r w () Yx,w () Yx B x rr r ,wwh () = () ¥ () = • Â 1 eF q i n ij j j n == = Â 1 1 1, , , ZePi n iijj j n == = Â 1 1, , , Condition Monitoring; Condition-Monitoring System(s); Engine Condition Monitoring; Engine Condition–Monitoring System(s) C-327 1. Balance the shaft as a rigid body. 2. Balance for each critical speed in the operating range. 3. Balance out the remaining noncritical modes as far as possible at the running speed. Balance planes picked are the ones where maximum amplitudes of vibration occur. Modal balancing has severe limitations. Calculated values for mode shapes and natural frequencies must be computed. Input data may limit the accuracy of these figures. Then, when damping is significant, such as in the case of fluid film bearings, problems arise. Damped modes look very different from undamped ones, so predicting modes and frequencies can be a severe problem. No one has overcome this to the extent that this method can be used as influence coefficients can in modern balancing machines. Surge Control; Pressure and Flow Transducers Optimum performance of driven equipment (compressors and pumps) enhances delivery of revenue product. A great deal of effort is, therefore, spent determining the parameters that affect turbomachinery performance. These include capacity, pressure ratio, power (and therefore fuel) consumed, and the surge characteristics of the machine. Surge describes the condition when pressure at the suction drops to the extent that the flow reverses on itself. In a compressor, it first occurs on individual blades. This is called stall or rotating stall. Fully developed rotating stall is surge. In a pump, the surge phenomenon is called cavitation. Both surge and cavitation destroy equipment in what may be disastrous failures. C-328 Condition Monitoring; Condition-Monitoring System(s); Engine Condition Monitoring; Engine Condition–Monitoring System(s) FIG. C-354 Typical principal modes for a symmetric and uniform shaft. 13 Performance analysis of driven equipment, whether done for test or for normal operation, generally requires that the following readings be taken: 1. Inlet temperature 2. Inlet pressure 3. Discharge temperature 4. Discharge pressure 5. Compressor speed 6. Atmospheric pressure 7. Differential pressure across the flowmeter 8. Temperature at the flowmeter 9. Pressure at the flowmeter 10. Fluid (gas, liquid) properties The preceding properties determine the mass flow through the machine, based on volume flow, pressure and temperature readings, and fluid properties. The gas properties help work out the revenue base for the delivered fluid. For instance, gas may be sold to customers based on a certain heat value per unit time. Mass flow ¥ calorific value of fuel per unit mass = heat delivered per unit time As field composition changes, molecular weight frequently changes so gas composition analysis should be done regularly. If done frequently, changes in gas composition may provide early warning of a declining field. All flow and pressure measurement devices require certain minimum lengths of straight pipe prior to measurement stations. A length of 10 pipe diameters is considered good practice. If piping is protracted and tortuous, accurate measurement may be difficult. Valves in the system must have the right closure speed characteristics and leak-tight properties. Pressure measurement Pressure measuring devices include the following: 1. Pitot static tubes 2. Pressure transmitters and transducers 3. Barometers 4. Liquid manometers During commissioning, startup screens are used to protect the machine against welding slag and other inclusions left in the piping during construction. They cause a sizable differential drop, however, and should be removed. Manometers are frequently used to measure differential pressures and atmospheric pressure. They should be calibrated regularly. It is important to watch for trapped bubbles within the liquid because they can make a reading inaccurate. Inlet and discharge pressures are the sum of the static pressure and the velocity pressure at the respective points. Flow transducers Fluid (gas and liquid) flow through compressors and pumps (driven equipment) is measured by appropriate measuring transducers. These transducers include: Condition Monitoring; Condition-Monitoring System(s); Engine Condition Monitoring; Engine Condition–Monitoring System(s) C-329 1. Venturi tubes. These consist of a convergent section at the entrance, a constant diameter throat, and a divergent section. They are accurate but hard to retrofit. They should be planned for in advance. 2. American Society of Mechanical Engineers (ASME) flow nozzle. This is essentially little used in the field as it is hard to fit in a process plant. It works well in test rigs. Items 1 and 2 handle about 60 percent more flow than orifice plates. 3. Orifice plates. Orifice plates are mostly the concentric orifice type, although an eccentric orifice might be used, depending on the quantity of fluid to be measured. 4. Elbow flowmeters. Centrifugal force at the elbow is used to find the difference between the inside and the outside of the elbow. This is then related to discharge pressure. There are many other techniques that are more theoretical, better suited for lab work, or require complex data to be supplied by the OEM. Nonintrusive Wear Monitoring Nonintrusive wear monitoring is a technique where neutron bombardment is used to determine the state of wear of a bearing in a nonintrusive wear. The technique was pioneered on lower-temperature machinery such as diesels. Although it is dropping in price, it is still expensive. The wear monitors are relatively bulky, which has not helped their popularity. Since its introduction, vibration techniques and performance analysis techniques have developed well and dropped in price. It is unlikely that nonintrusive wear monitoring will ever rival contemporary vibration and temperature monitoring for detecting bearing failures. It may make a comeback when development budgets are not tight. References and Additional Reading 1. Soares, C. M., “Aspects of Aircraft Engine Monitoring Systems Experience as Applicable to Ground Based Gas Turbine Engines,” TMC, 1988. 2. Soares, C. M., “Design, Installation and Operation of Turbomachinery in Western Canadian Gas and Oil Production,” ASME IGTI, 1981. 3. Lifshits, Simon, and Smalley, “More Comprehensive Limits for Rotating Machinery,” ASME Journal for Gas Turbines, vol. 108, October 1986. 4. Lifson et al., “Assessment of Gas Turbine Vibration Monitoring,” ASME-GT-204. 5. Floyd, “Key Issues and Technology for Future Programs,” Proceedings Fifteenth Annual SFTE Conference. 6. “An Overview of Airborne Vibration Monitoring (AVM) Systems,” Society of Automotive Engineers, SAE 871731. 7. Vibration seminar notes, Mechanical Technology Incorporated. 8. Aspects of Flexible Rotor Balancing, 2d ed., Schenk Treble, January 1976. 9. Simmons and Smalley, “Effective Tools for Diagnosing Elusive Turbomachinery Problems in the Field,” ASME 89-GT-71. 10. Balancing of Jet Engines, Schenk Treble, A1511. 11. Soares, C. M., “Vibration Analysis: Separating the Elements of Machinery, Process and Personnel,” TMC, 1992. 12. Soares, C. M., “Latest Techniques in Repair Technology,” TMC, 1990. 13. Boyce, turbomachinery course notes, 1979. 14. Soares, C. M., “Condition Monitoring,” Asian Electricity, 1997. 15. Bloch, H., machinery failure analysis and troubleshooting course notes. 16. Gunter, “Rotor Bearing Stability,” Proceedings First Turbomachinery Symposium, 1972. 17. Thomson, Mechanical Vibrations, 2d ed., Prentice Hall, Englewood Cliffs, NJ, 1961. 18. Buscarello, R., vibration course notes, 1980. 19. Handbook on vibration, McGraw-Hill, New York. 20. Bloch, H., and Soares, C. M., Turboexpanders and Process Application, Gulf Professional Pub., 2001. Control Regulators (see Actuators) C-330 [...]... Control Systems; Controls FIG C- 376 The PQ2000 system offsets voltage disturbances caused by storms, thereby preventing costly production -equipment shutdowns (Source: Mechanical Engineering Power, ASME, November 19 97. ) FIG C- 377 Schematic for the wearing of the PQ2000 (Source: Mechanical Engineering Power, ASME, November 19 97. ) Control Systems; Controls C-353 FIG C- 378 Network problems caused by the... factory’s annual electrical costs from a high of $110,000 to $120,000 down to $60,000 to $70 ,000 (see Figs C- 376 and C- 377 ) Using this system to correct a 2-s power outage can save a semiconductor manufacturing plant $70 ,000 in product that would otherwise be lost The same 2-s interval can cause $600,000 in data processing losses for a computer center, require weeks of cleanup in a glass plant, or corrupt... storms’ slight voltage disturbances These brief voltage sags can disrupt process electronics, resulting in losses in production and costly downtime to recalibrate and restart the * Source: Adapted from extracts from “Compensating for Lightning,” Mechanical Engineering Power, ASME, November 19 97 C-350 Control Systems; Controls FIG C- 375 Speed response of the gas turbine and the generator with and without... power supply can have expensive consequences for the process engineer A 2-s power interruption in a semiconductor plant cost over $70 ,000 in 19 97 dollars The following* cases illustrate the costs associated with power fluctuations The power behind thunderstorms can cause problems for industrial facilities where electronic systems that control critical equipment are sensitive to the storms’ slight voltage... storms’ slight voltage disturbances These brief voltage sags can disrupt process electronics, resulting in losses in production and costly downtime to recalibrate and restart the * Source: Adapted from extracts from “Compensating for Lightning,” Mechanical Engineering Power, ASME, November 19 97 Control Systems; Controls C-351 equipment A pilot project funded by Oglethorpe Power Corp in Tucker, Ga.,... The pump-wheel 7 of the turbo coupling is connected to the flanged sleeve (input) and the turbine wheel 8 is connected to the flanged-shaft (output) The acceleration of the gas turbine results in a speed difference between the coupling wheels that generates a torque as shown in Fig C 372 The torque is almost proportional to the slip (See Fig C- 374 .) C-350 Control Systems; Controls FIG C- 375 Speed response... power supply can have expensive consequences for the process engineer A 2-s power interruption in a semiconductor plant cost over $70 ,000 in 19 97 dollars The following* cases illustrate the costs associated with power fluctuations The power behind thunderstorms can cause problems for industrial facilities where electronic systems that control critical equipment are sensitive to the storms’ slight voltage... relatively high inertia (Fig C- 371 ) For this application the turbo coupling must meet the following design criteria ᭿ Rapid torque buildup with increasing slip ᭿ High availability Figure C- 372 shows the torque transmission of a turbo coupling versus slip for generator speeds of 3000 and 3600 rpm Brake properties at high speed and acceleration C-348 Control Systems; Controls FIG C- 371 Gas turbine drive with... Control Systems; Controls A control system is what controls and governs an operating system or part of that system The field of controls and control systems is wide enough to fill several handbooks on its own However, in this more general book, we shall attempt to highlight certain common aspects and systems of process controls with examples We have selected systems that have, when malfunctioning, missing,... compressor from operating in an unstable range or at other hazardous conditions ᭿ Process: to adapt the compressor performance to the demands of the process * Source: Sulzer-Burckhardt, Switzerland Adapted with permission C-332 Control Systems; Controls FIG C-356 Electronic control cabinet (Source: Sulzer-Burckhardt.) FIG C-3 57 Example of a monitoring panel (Source: Sulzer-Burckhardt.) The control systems . Automotive Engineers, SAE 871 731. 7. Vibration seminar notes, Mechanical Technology Incorporated. 8. Aspects of Flexible Rotor Balancing, 2d ed., Schenk Treble, January 1 976 . 9. Simmons and Smalley,. Turbomachinery Symposium, 1 972 . 17. Thomson, Mechanical Vibrations, 2d ed., Prentice Hall, Englewood Cliffs, NJ, 1961. 18. Buscarello, R., vibration course notes, 1980. 19. Handbook on vibration,. through C-3 57. ᭿ Safety: to prevent the compressor from operating in an unstable range or at other hazardous conditions ᭿ Process: to adapt the compressor performance to the demands of the process FIG.