Improving Machinery Reliability 3 Episode 4 ppt

Machinery Reliability Audits arid Reviews 109 EQUIVALENT SYSTEM WODE GRAPES WODE XO. 1 31.80 HZ ieo7.e3 CPW 1 WODE XO. 2 114.49 HZ 6869.44 CPY WODE XQ. 3 307.04 HZ 18476.23 CPW WODZ WO. 4 382.29 HZ 2~37.17 CPW Figure 3-23. Torsional natural frequencies and mode shapes. An interference diagram for the turbine-driven compressor with a gear box is given in Figure 3-24. The rated speeds are 5,670 rpm for the gas turbine and 10,762 rpm for the compressolr. In this system, excitation at 1X and 2X the gas turbine and compres- sor speeds are possible. The 1X excitation of gas turbine speed excites the first critical speed at 1,907 rpm; however, it will not reach the second natural frequency at 6,869 rpm since maximum speed would be less than 6,000 rpm. The compressor speed (1X) excitation would excite the first torsional natural frequency at 1,005 rpm and the sec- ond natural frequency at 3,619 rpm on the gas turbine. Once the system has been modeled and the natural frequencies have been deter- mined, the forcing functions should be applied. The forcing functions represent dynamic torques applied at locations in the system that are likely to generate torque variations. Identification of all possible sources of vibration is an important step in diagnosing an existing vibration problem or avoiding problems at the design stage. The most likely sources of dynamic torques include reciprocating engines, gears, fans, turbines, compressors, pumps, motors (synchronous and induction), couplings, fluid interaction (pulsations), and load variations. 110 Improving Machine9 Reliability N I > 0 z W 3 0 W lx LL I- z 0 ln W LY J U z 0 H v) (*: 0 I- I Figure 3-24. Interference diagram for gas turbine-compressor train. To evaluate the stresses at resonance, the torsional excitation must be applied to the system. For systems with gear boxes, a torque modulation of 1%, zero-peak is a representative torque value that has proven to be appropriate for most cases. As a rule of thumb, excitations at the higher orders for gears are inversely proportional to the order numbers: the second order excitation is 0.5%, the third is 0.33%, etc. The torque excitation should be applied at the appropriate location and the torsion- al stresses calculated on the resonant frequency and at the running speed. An exam- ple of the stress calculations of the second natural frequency resonance is given in Table 3-5. It shows that a 1% torque excitation on the bull gear would cause a maxi- mum torsional stress of 4,179 psi p-p in shaft 9, which is the compressor shaft between the coupling and the first-stage impeller. The dynamic torque modulation across the couplings is calculated for the applied input modulation. For this mode, the maximum torsional vibrations occur across the compressor coupling and the dynamic torque modulation was 2,626 ft-lb. Variable Speed Drives. Units that use a variable speed drive in conjunction with an electric motor will have excitation torques at the running speed frequencies, and at sev- eral multiples, depending upon the design of the variable speed dri~e.2~ Figure 3-25 gives an interference diagram for one such system. It is difficult to remove all coinci- Machinery Reliability Audits and Reviews 111 Table 3-5 Torsional Stress Calculations at the Second Torsional Natural Frequency for 1 % Excitation at the Bull Gear Dynamic torques (lob zero-peak) applied at the bull gear Maximum resultant torsional stresses at the 2nd torsional resonance 6,869.44 cpm Stress psi P-P Stress Shaft psi P-P scf I 2 3 pi* 5 6* 7 8* 9 10 11 12 13 14 15 16 17 18 19 3.92 34.47 117.23 Dynamic torque variation 21.76 Gear mesh I.334.81 Dynamic torque variation 1,393.16 859.02 723.70 582.18 564.75 434.23 422.73 41 1.05 3 14.94 215.28 98.88 2.00 I .50 3.00 3.00 3.00 3.00 1.50 1.50 I .50 I .50 1.50 1.50 1.50 1.50 1.50 I .50 7.83 51.71 35 I .68 65.27 4,004.43 4,179.49 1,288.52 1,085.55 873.27 847.12 65 1.35 634.09 6 16.57 472.41 322.93 148.32 468.82 ft-lbs 2,626.80 ft-lbs ~~ ___ Note: xValires cire clyircriiiic torque vnriatiori across coupling or gear, fi-lbs 880 L r " w 0 a L r 5 4e8 5: a 2 z B :: - 200 288 IEB 600 I008 WERAIING SPEED. RPH Figure 3-25. Interference diagram for induction motor with variable speed drive. 112 Improving Machinery Reliability dence of resonances with the excitation sources over a wide speed range; therefore, stress calculations must be made to evaluate the adequacy of the system response. Reciprocating Machinery. For reciprocating units such as compressors, pumps, or engines, the harmonic excitation torques must be calculated and applied at the appro- priate shaft location to calculate the stresses.25 Allowable Torsional Stresses. The calculated torsional stresses must be compared to applicable criteria. The allowable values given by Military Standard 164 are appropriate for most rotating equipment. The allowable zero-peak endurance limit is equal to the ultimate tensile strength divided by 25. The MIL Spec uses this as a global derating factor rather than calculating on the basis of individual factors accounting for keyways, surface roughness effects, and the like. When comparing calculated stresses to this value, the appropriate stress concentration factor and a safety factor must be used. Generally, a safety factor of 2 is used for fatigue analysis. When these factors are used, it can be shown that fairly low levels of torsional stress can cause failures, especially when it is observed that the standard keyway (USA Standard ANSI B17.1) has a stress concentration factor of 3. We should not lose sight of the fact that process machinery is expected to live much longer than military hardware, and that our process machinery manufacturer has, perhaps: 1. no S-N curves 2. no intention of applying individual derating factors for either known stress rais- 3. no interest in determining coupling and misalignment-induced stress adders, etc., It would thus be reasonable to use a global derating value of 75, and, indeed, world-class turbomachinery manufacturers such as Elliott, Dresser-Rand, Mannes- mann-Demag, Sulzer, Mitsubishi, and surely many others, have both the experience and analytical capability to virtually guarantee unlimited life of turbomachinery shafts operating at relatively much higher mean torsional stresses. A typical example would be steam turbine shafts with tensile strengths of 105,000 psi (ult.) and steady- state torsional stresses of 10,900 psi, where this latter stress simply uses the standard calculation formula ers or unknown superimposed stresses Nevertheless, 2,,,,/75 is not at all unreasonable for machines built by the “other” manufacturers. A midwestern U.S. plant uses rotary blowers direct-coupled to 200 hp, 1800 rpm motors. The blowers came with 2% inch diameter shafts that had an ultimate strength in tension of 80,000 psi. Although nominal stresses are thus only 2281 psi, the plant experienced many shaft failures with derating values as high as 80,000/2281 = 35. A typical torsional stress allowable thus becomes the ultimate ten- sile strength divided by 75. Machinery Reliability Audits and Reviews 113 Transient Torsional Analysis After the steady state analysis is made, a transient analysis should be made to evaluate the startup stresses and allowable number of startups for synchronous motor systems.22,26 The transient analysis refers to the conditions on startup, which are con- tinually changing because of the increasing torque and speed of the system. When a synchronous motor starts, an excitation is imposed upon the torsional system due to field slippage. As the motor increases in speed, the torsional excitation frequency decreases from twice power line frequency (typically 120 Hz) linearly with speed toward zero. During this startup, the torsional system will be excited at several of its resonant frequencies if they are between 0 and 120 Hz, as shown in Figure 3-26. The response amplitudes and shaft stresses depend upon the resonant frequencies, the average and pulsating torque when the system passes through these resonant fre- quencies, the damping in the system, and the load torques. The startup analyses can be made for loaded or unloaded operation. The transient response is also affected by the starting acceleration rate of the motor. For slow motor startups, the system will stay at a resonant frequency for a longer period of time, allowing stresses to be amplified. If acceleration is rapid, passing through the resonance quickly will mini- mize the amplitude increase at resonant frequencies. Synchronous motors develop a strong oscillating starting torque because of slip- page between the rotor and stator fields. Although this is only a transient excitation, the pulsating torque can be strong enough to exceed the torsional endurance limit of Figure 3-26. Torsional stresses introduced into motor shaft during synchronous motor startup. 114 Improving Machinery Reliability the shaft. For this reason the transient stresses must be calculated and compared to the endurance limit stress. It is not necessary that the transient stresses be less than the endurance limit stress; however, the stresses must be sufficiently low to allow an acceptable number of starts. If the transient stresses exceed the endurance limit, the cumulative fatigue concept is applied to the stresses in excess of the endurance limit stress to determine how many starts can be allowed for the system. Cumulative fatigue theory is used to estimate the number of cycles a certain stress level can be endured before shaft failure would occur. This is based upon a plot of stress versus number of cycles (S-N curve), which defines the stress conditions at which a failure should occur. The S-N curve is based upon actual tests of specimens of a particular type of metal and defines the stress levels at which failures have occurred in these test specimens. These S-N curves are available for most types of shafting materials. Using the appropriate curve, the allowed number of cycles for a particular stress can be determined. It is possible to calculate the number of total startups that can be made with the system before a shaft failure is predicted. Since the stress levels vary both in amplitude and frequency, a more complex calculation must be made to determine the fraction of the total fatigue that has occurred. The stress levels for each cycle are analyzed to determine the percentage of cumulative fatigue and the allowable number of startups can then be determined. The calculation of the allowable number of starts is strongly dependent upon the stress versus cycles to failure curve and whether torsional stresses higher than the torsional yield are allowed. In the design stage it is preferable to design the system such that the introduced torsional stresses do not exceed yield. This can usually be accomplished through appropriate coupling changes. Impeller and Blade Responses A design audit should also include an assessment of the potential excitation of blade or impeller natural frequencies. Several papers document such The impeller and blade response analysis should include: 1. The blade and impeller natural frequencies 2. The mode shapes 3. Interference diagram indicating potential excitation mechanisms and the natural frequencies. The interference diagram, which gives the blade and impeller natural frequencies and the various potential excitation mechanisms, is the key to prevention of failures. The resonances should be sufficiently removed from the major excitations in the operating speed range. In the design stage, it is possible to calculate the natural frequencies and mode shapes using finite element method [FEM] computer programs. However, the accu- racy of predictions depends to a great extent upon the experience of the analyst and the complexity of the system. Since the blades and impellers will usually be available in advance of the rotor assembly, the most accurate natural frequency and mode shape data can be obtained Machinery Reliability Audits arid Reviews 115 from shaker tests or by modal analysis methods. The modal analysis technique uses a two-channel analyzer and an impact hammer and accelerometer to determine the nat- ural frequencies and mode shapes. For example, the natural frequencies and mode shapes of a centrifugal impeller were measured using modal analysis techniques (Figure 3-27). When these frequencies were compared to values determined from a shaker study, good correlation was obtained. The mode shape for the two-diameter mode is given in Figure 3-28. An interference diagram for this impeller is given in Figure 3-29. Note that poten- tial excitation mechanisms include vane passage frequency (1 5X) and two times vane passage frequency (3OX). It is sometimes impossible to completely avoid all interferences over a wide speed range, since there are so many natural frequencies. For most systems, in order for a failure to QCCU~, several things usually occur together. First, there must be a mechan- ical natural frequency. Second, there must be a definite excitation frequency, such as vane passing or diffuser vane frequency. Third, there must be some acoustical reso- nant frequency that amplifies the energy generated; and fourth, there must be the appropriate phase relationship that causes the pulsation to cause a shaking force on the impeller or blade. The best way to avoid such problems is to avoid coincidence of the resonances with the excitation mechanisms. Figure 3-27. Natural frequencies of centrifugal impeller. 116 Improving Machinery Reliability Figure 3-28. Two-diameter mode shape for centrifugal impeller at 1,360 Hz determined by modal analysis tests. 5000 30X I CIR 4 DIA 4000 N I- I > :: 9 3000 3 DIA Y 0 W a: -1 U 3 U I5X P 1 2000 p: W J -I 0 CIR L z 2 DIA U I000 1 DIA 0 0 2000 4000 6000 8000 10000 RUNNING SPEED, RPH Figure 3-29. Interference diagram for centrifugal impeller. Muchinery Reliability Audits arid Reviews 117 Pulsations Pulsations can cause problems in rotating equipment as well as reciprocating ma~hinery.~'.~* Pulsation resonances occur in piping systems and are a function of the fluid properties and the piping, compressor, or pump geometry. Pulsations can cause premature surge in centrifugal compressors and pumps if the generated pulses, such as from stage stall,I6 match one of the pulsation resonances of the system. The potential pulsating excitation mechanisms for piping systems are the running speed component and its multiples, vane, and blade passing frequency and those caused by flow excited (Strouhal frequency) phen~mena.'~ In the design stage, the acoustical natural frequencies of piping systems can be calculated using either digital2s or analog modeling proced~res.~' A model of a pip- ing system analyzed on a digital computer is given in Figure 3-30. The predicted Test Points A- B- c- D- E- F- C- K- 1- Cylinder 41 PDF PDL ClO6ed End of Bypass Hotrder Take-Off HeLer Run Inlet Flng 3' b4 Meter PDM Pump t2 Blocked Figure 3-30. Digital computer model of pump system for pulsation analysis. 118 Improving Machitiery Relinbiliry pulsations in the reciprocating pump system at selected locations are given in Figure 3-31. These pulsation levels define the energy in the pump and the piping shaking forces, and can be used to define the necessary piping supports and span lengths to achieve acceptable vibration levels. The program can be used to redesign the piping to reduce the pulsations to acceptable levels. Summary and Conclusions Rigorous rotordynamic analyses must be thought of as additional insurance that the machinery will run without major problems. Many of the analysis procedures and computer programs that have been developed are being used by both the manufactur- er and by consultants who offer these design audit services. As with many computer programs, the interpretation of the computer results is dependent upon the skill and 2 Figure 3-31. Predicted pulsations in pump and piping system for pump speed range of 170-260 rpm. [...]... and design Pnspection and quality control Cooling oil system 3 2 2 3 3 2 1 I VendorX VendorY 4 4 4 8 1 VendorX 8 5 4 I I I I 2 2 2 5 6 6 6 4 6 6 1 2 2 I 8 I 6 4 1 Value x Rank 8 I 5 5 6 6 I 5 8 6 VendorY 12 8 8 24 21 14 5 6 6 6 8 12 12 5 9 9 14 8 4 Total 8 12 180 Value scale: 3 = very important 2 = average importance 1 =below average 24 10 8 24 21 IO 5 6 6 I 10 16 12 5 18 18 8 208 Ranking scale: 10 =perfect,... pertinent findings reflect in the next issue of Machinery Reliability Audits arid Reviews 1 23 Figure 3- 34 Distribution of gas turbine component damage (Courtesy Der Maschinenschaden, No 1 53, 1980.) Figure 3- 35 Distribution of primary causes of failure for industrial gas turbines (Courtesy Der Maschinenschaden, NO 1 53, 7980.) 1 24 Improving Machinery Reliability Table 3- 7 Primary Causes of Gas Turbine Failures... location: 38 2 Pumps repaired at own shops: 267 Pumps repaired at outside shops: 119 Failure Causes Repaired on Site Repaired in Shop Mechanical seals Bearing distress Vibration events Packing leakage Shaft problemskouplings Case failure/auxiliary lines Stuck Bad performance Other causes Total 112 72 8 1 03 21 35 20 1 53 83 13 22 60 2 4 17 38 2 13 18 22 38 6 Machinery Reliability Audits and Reviews 125 Table 3- 9... Bladeslimpellers Thrust bearings Compressor seals Motor windings Diaphragms Miscellaneous causes All causes 22% 21% 13% 8% 6% 6% 3% 1% 20% 100% I22 4 28 110 22 48 200 35 0 I0 44 42 26 I6 12 I2 06 02 40 2.00 HrsNr 54 2 7 18 3 6 12 7 28 I37 hours problem-cause distribution and duration are shown in Table 3- 6 The table also shows where detailed design reviews might prove most profitable Experienced process plants... PD- Ps = 2,000 - 30 0 Plunger diameter =9cm (z)(81> Plunger area 4 = 63. 8 cm2 Net effective plunger force = (1,700) ( 63. 8) = 108,200kg 3 Determination of maximum gas force in a representative second stage PD - Ps = 3, 600 - 1,750 Plunger diameter = 1,850 kg / cm2 (= net effective pressure) =8cm (M 64) = 50 .3 cm2 Plunger area _ 4 Net effective plunger force = (1,850) (50 .3) = 93, 000 kg 4 Inertia load contribution... Figure 3- 34 gives the distribution *Leopold, J., “Erfahrungen Mit Stationaren Gasturbinen Moderner Bauart,” Der Mascliinrtischarlen, Vol 53, No 5, 1980 122 Ittprovittg Macltittery Reliability Figure 3- 33. Shaft riding brushes in turbine-generator application (Courtesy of Sohre Turbomachinery Inc., Ware, Massachusetts.) of primary failure causes for industrial gas turbines from 1970 to 1979 Figure 3- 35... 29 Hydrostatic test logs 30 Mechanical run test logs including: a Qil flows, pressures, and temperatures 138 Improving Machinery Heliability b Vibration including X-Y plot of amplitude versus rpm during startup and shutdown c Bearing-metal temperatures d Observed critical speeds 3 1 Rotor-balance logs 32 Rotor mechanical and electrical run-out 33 “As-built” API data sheets 34 “As-built” dimensions (including... blade tip 3 Rotor assembly drawing, including: a Axial position from active thrust-collar face to: 1 Each wheel (inlet side) 2 Each radial probe 3 Each journal-bearing centerline 4 Key phasor notch b Thrusk-collar assembly details, including: * 1 Collar-shaft fit with tolerance “2 Concentricity (or axial run-out) tolerance 136 Improving Machinery Reliability 3 Required torque for locknut 4 Surface-finish... for inertia forces acting at a particular crank angle These calculations lead to a tabulation of CYl A Gas Load “ A A lnerlia Forces “)1 36 0’ I Figure 3- 37 Forces acting on first stage of typical hyper compressor  142 Improving Machinery Reliability Cyl c Figure 3- 38.Forces acting on a second stage of typical hyper compressor design conservatism for selected components The actual factor of safety built... operation of major machinery These logs should be retained for future reference  132 Improving Machinery Reliability 29 Rotor-balance logs Rotor-balance target values given by the manufacturer can be compared with minimum requirements quoted in the literature Figure 3- 36 shows a typical comparison chart Rotor-balance logs should also be retained in the purchaser’s equipment records 30 Rotor mechanical . 21.76 Gear mesh I .33 4. 81 Dynamic torque variation 1 ,39 3.16 859.02 7 23. 70 582.18 5 64. 75 43 4 . 23 42 2. 73 41 1.05 3 14. 94 215.28 98.88 2.00 I .50 3. 00 3. 00 3. 00 3. 00 1.50 1.50. 1.50 1.50 1.50 I .50 7. 83 51.71 35 I .68 65.27 4, 0 04. 43 4, 179 .49 1,288.52 1,085.55 8 73. 27 847 .12 65 1 .35 6 34 .09 6 16.57 47 2 .41 32 2. 93 148 .32 46 8.82 ft-lbs 2,626.80 ft-lbs. causes 22% 21% 13% 8% 6% 6% 3% 1% 20% I22 4 28 110 22 48 200 35 0 I0 .44 .42 .26 .I6 .12 .I2 .06 .02 .40 100% 2.00 54 2 7 18 3 6 12 7 28 I37 hours - problem-cause