AstudyoftheNewkirkeffectinturbomachinery

A. D. DIMAROGONASLehigh university, Betnienem, Perm. (V.S.A.)(Received January 29, 1974)SUMMARYAn analytical and experimental study was undertaken on the Newkirk Effect as annlied to tnrhomarhinerv whir.h i ihet vihratinn chanoe. nrodurH when a hiffh 置隹 一 垂看 ，_ 一 申擎争， 賺擎 jf ，賢爭幸 _ speea rotor rubs on stationary components due to the uneven distribution of the produced heat around the rotor. The analysis predicted three possible modes of the-Newkirk -Effeetc-spiralling, osciHatory and constan卜 modes.The first 4s as- sociated with very high vibration amplitudes and the latter two with low amplitudes， even vibration suppression and may be considered as stable modes.To support and veriTy analyst an expenrhehtaV was coristrucfed and a limited number of tests conducted. The test results verified both quantitatively and qualitatively the analytical findings for the modes of the Newkirk Effect. The parameter study indicated that stability of the system does not depend explicitly on whether the running speed is below or above the critical speed，but rather on the phase angle between static and dynamic bow. This is a dynamic property of the system unrelated to the friction characteristics. It depends, to a lesser extent, upon the amount of generated heat and the other characteristics of the system. The clearance-was -found to-be a very important factor. The existence of a- threshold value of the clearance was demonstrated.INTRODUCTIONOne of the main objectives in the design of modern machines is the reduction of weight and improvement in quality. This improvement has introduced high rotating speeds, velocities, deflections and flexibilities of the macmnes members, and designers are now facing new problems not always considered before.The direction of designing over-tuned rotating members，i.e., with the operating speed lower than the first eritieal speed, -is no -i&Rger-followedT -Modern machines operate above the first critical speed and very often above the second or third. The supports and foundations become flexible，too, and their natural frequenciesinterfere sometimes with the operaring speeds. The amjrffficraikm factor合 become lower，but there are starting problems when passing through the critical speeds. To oring the unbalance response within acceptable limits, dynamic balancing is usually enough. New precise balancing methods have been created1，but as theNEWKIRK EFFECT IN TURBOMACHINERY373speeds and the transmitted forces and torques are increasing, the designer faces additional dynamic problems which are sometimes unpredictable and usually uncor- rectable, e.g” fluid and structural instabilities. A classification of the dynamicproblems in machine design is given by Rieger2 and Gunter3.seals and oil deflectors, which are used to separate two fluids and to ensure mechanical limitations. When rotating parts come in contact with the stationary elements, heat is generated which deforms the parts, and Unbalance and vibration is finally produced4. At other times，due to the normal or accidental presence of fluids in the gaps between rotating and stationary components，heat can be generated due to an abnormal flow of these fluids，or the abnormal energy dissipation in their volume with the same results as above.The usual form of seal, subject to rotor rubbing phenomena, is the labyrinth type used in turbines. With these seals the designer has a choice between materials which wear quickly and have a low coefficient of friction, or harder materials which resist wear but have a high coefficient of friction. The materials selected must meet additional requirements，such as corrosion and erosion resistance, high thermal conductivity，and strength in high temperatures. In the case of contact between stationary aiid rotating parts, considerabie forces can appear as friction forces or shock forces in the case of violent interaction5. The sum of the influences of the heating unbalance，and the direct forces，can have either an amplifying or a stabilizing effect. In the case of amplification，a continuous increase in amplitude and phase angle is usually observed and a polar presentation of these quantities shows an outward spiral curve6.The rotating parts may also be surrounded by a fluid environment, which can exert considerable influence. The phenomena of fluid induced instabilities incases in which the rotors are working in fluid environment such as steam and gas turbines and pumps. Under certain circumstances, vibration can be induced bytrapped fluids within the annuii between stationary and rotalittg parts7.Vibration can also be initiated or amplified by structural instabilities arisingFig. 1. Geometry of rotor-packing interaction*from the transmitted forces (buckling)，or torques (torsional buckling).The Newkirk Effect occurs when a rotating shaft R (Fig. 1), due to its bow， 021，and due to the displacement of its center of rotation from O to O, comes in contact with a stationary part, S. In the above model, circular and synchronous orbit of the geometric center of the rotor Q2 about O, has been assumed At angle on the contact is at point B which moves on the rotor circumference between points C and B. A portion of the friction heat generated goes into the rotor between B and C and bows the Totor because the resulting temperature field is nonvmnorm. Depending on the dynamic characteristics of the rotor, vibration can decrease (if the unbalance is in location Uz), or increase (if the unbalance is in location U). Generally there is also a phase shlffbetween the position of tne original bow and the location of the produced thermal bow which can be synthesized vectorially, so that the result is a spiral pattern converging or diverging, respectively.In the latter case； the result is usually severe damage to the interacting parts sometimes leading to catastrophic failures. In recent years，many such incidents have been reported in a variety -of macnmes-such as steam and gas turbines， pumps，compressors and aircraft engines.The demands of increasing efficiency do not permit higher operating clearances- Thas, the designer has only one way to gor to know the mechanism of the Newkirk Effect and the significance of the several design parameters in order to relate the operation of the machine with the safe or the less dangerous selection of these parameters.ECTTHE NEWKIRKThe Newkirk Effect has been recognized and reported since 1925s for a vertical hvHrnelectrir tnrhinp-apnertnr anH inturhines4 1 he nrohlem though, wasJ 一勢等- - 看胃 爭 一 一 ”_ 一一 一 痛 一 一一一 X一 - C/ 9 *not signincant at tnat time because the rotors were very stiff and short, and could maintain the clearance to avoid rubbing. But as the rotors became longer and more flex4ble4he ruboing phenomenon became considerable； Recently, manyrotormbbing phenomena have been reported in a variety of large macnines, such as steam turbines，gas turbines，compressors and pumps. rhe Newkirk Effect is cfosery related to the efficiehcy of the madiine会 Vh6r， to provide effective sealing，very tight clearances must be maintained, while to avoid rubs the clearances must be high. The alternatives are: low generated heat, high clearances, and iow efficiency，versus high generated heat, tight clearances and improved efnciency. As mentioned before, the selection of the packing materials forNewkirk4 noticed first the thermal character of the phenomenon and gave a correlation with the critical speeds. Tests were made at the same time by Taylor10 to verify the hypothesis of Newkirk Hiat rubbing instabilityoccurs below the critical speeds，while above the critical speed there is a self-stabilizing effect because of the reversal of the phase angle between the exciting force (unbalance due to thermal deflection) and tlie dyhamic deflectionV Taylor used a ifcbent shaft modeir7t0. When light rub was applied below the critical speed，the amplitude built up slowly at first and then more rapidly. Tests above the critical speed showed that with light rubbing the vibration level decreased. Newkirk and Taylor also noticed a “backwardrubbing whip” in tests when the rubbing accidentally became very hard. The direction Of rotation and its speed was slightly higher than the rotors critical speed. An explanation of this can be given by considering the friction forces developing at the rubbing. These forces at higher speeds have little effect, because the heatpropagation- is-so -rapid-that- theif cifect-is-minimized.Kroon and Williams6-9 observed the spiral character of the Newkirk Effect and tried to correlate the experimental results empirically to provide an analytical tool for prediction of the rubbing response/ The author11 presented an analytical method to compute the rubbing response of a hollow cylinder，rotating in a clearance annulus and supported by orthotropic bearings. This method permits the calculation of the static and dynamic bow in time，in a coordinate system affixed to the rotor，given the properties and geometry of the system. Some general results have been derived from tnis stuHy：(a) The system response can have the three modes:(a.l) The spiralling mode. The amplitude and phase angle are increasing continuously up- to somo point where the amplitude varies harnionicaHy around a maximum value while the phase angle increases continuously-(a.2) The oscillatory mode. The amplitude oscillates around a value close tothe lnitianjow of the system.一 一(a.3) The constant mode- The amplitude reduces to a constant value where it remains, with the phase angle having the same behavior.(b) This response can be initiated only by an initially unbalanced or bowed(c) The mode of the Newkirk Fffect depends primarily on the dynamic response of the system, namely the phase angle between static and resulting dynamic bow at the operating speed. It also depends on the friction characteristics，but thiseffect is secondary.- 一 In this paper，the method was used to derive general features of the Newkirk Effect and compare analytical and experimental results.EXPERIMENTAL INVESTIGATIONThis analysis was intended to be applied to actual high speed rotating machinery，where rubbing problems occur. However，to support the analytical study, an experimental set-up was used instead of real machines. The details of the system used are explained in ref. 11.The reasons for this decision were:(!) In real machines, it is difficult to control and measure the parameters of the system, such as generated heat and midspan vibration.(2) In the field，especially for large machines, it is difficult and very expensive to conduct tests:(3) Field testing required generally very long preparation.Therefore the test machine was built and equipped with an extensive instrumentation system to measure the dynamic response of the rotor. The method of initiating the rub was aimed at simulating the actual conditions in steam turbines, which is by gradually approaching the packing casing to the rotor. As theinteraction forces in real systems are unknown, the best way oi simulating a rub was to reproduce the actual phenomenon using similar rotor and packing designs. However, for analytical purposes this method involves an uncertainty in estimating the inputs to the analysis. To overcome this，the analysis did not use given heat inputs, as other analysts did before, but every attempt was made to obtain the most accuratemathematical.Heorrintinn of the nhvsirl mnHp.l Therefore thft analvds iirH 齡 _,，一 w 一 令M 一 隹 隹 M V V* _ J勢,inputs, physical quantities which can oe measured easily, sucn as the normal interaction force，the geometry of the system and the coefficient of friction. However， thereis stiHuncertainty about these quantities in such a complicated system： The coefficient of friction was estimated in a small scale test11 but it is known that such tests have very poor repeatability. The geometry of the annulus might be known at the beginning but ii cnanges because of the wear of the packing rings. Finally, tne normal force includes forces due to steam pressure and flow which are uncertain and cannot be calculated accurately.These uncertainties do not affect the main oojective of tms study，which was to determine if a system was stable or not. These factors specify the amount of generated heat，which controls the speed with which the system reaches the stable or unstable operation and not the stability or instability of the system itself.Also, the analytical results correlate very well with the test results and for the absolute response of the system.-Therefore， the decision to use this machine for verification of the analysis was justified.Dynamic responseThere are two ways to measure the dynamic response of the test rotor: (a) To add unbalance weights along the rotor corresponding to the bow configuration, (b) To measure the permanent bow which the rotor possesses as result of a previous severe rub. In this analysis，the second method was used. The measured run-out of the rotor was 0 0018 in. pck-to-pcak; therefore,-the permanent bow is 5=0.0009 in. The peak-to-peak amplitude of the rotor at several speeds divided by the initial run-out gives the amplification factor p. The phase angle between the static and dynamic high-spot of the rotor at 就vera卜speetis gives the phase angle C/ As “high“ spot” we define the point of the circumference of the rotor which has the highest distance from the center of rotation.The dynamic response was measured at the rubbir positfor in this casein the middle of the span. The results have been plotted in Fig. 2.The first critical speed of the system was at 1450 np.m. and the second critical was at 2400 r.p.m.KUDuing response The dynamic response of the system，given in Fig. 2, was used as input to the rubbing response calculation for three speeds: 1200, 1800； 3000 r.p.m. The first is a spirairing modeV the second is oscillatory and the third is converging mode- The results have been plotted in Cartesian form in Figs, 3, 4 and 5 respectively and in polar form in Figs. 6, 7 and 8.Fig. 4. Newkirk Effect at 1800 r.p.m.IaFig. 3, a typical unstable mode is shown. There are two calculated responses: wear = 0 means that the wear of the material is very small compared with the clearance and the how. Therefore, the heat generation continues for a long time and maintains the maximum bow of the rotor.Fig. 5. Newkirk Effect at 3000 r.p.m.NEWKIRK EFFECT IN TURBOMACHINERY379Fig. 6. Polar diagram at J20Q. r,p.HL.(spiral mode).Fig. 1. Polar diagram at 1800 r.p.m. (oscillatory mode).Fig. 8. Polar diagram at 3000 r.p.m. (constant mode).Wear = co means that the material wears so fast that the clearance is never less than the maximum vibration amplitude. Therefore，after the rotor bow reaches a maximum，the heat generation stops，the rotor cools rapidly and the bow returns to the initial value. This performance was actually observed in the tests because thenanlrino rino oncictcrf vrv thinnfKraccW 毳 l 赢轟毳矗應轟 K，毳纛廬 ,WA J V 纛息瀘知惠 VZ 纛A WjW# W f A AA WA A?f %毳V WA J V| V牵爲/ In Fig. 4, a typical oscillatory mode is shown. Again, because of the wear of the teeth the oscillatory motion predicted with the analysis did not appear in the tesrand forail praciicai purposes/ such performance can be accepted as stabie.In Fig. 5, a typical stable mode is plotted.In all modes, after a time，long enough to wear off the teeth，the rotor will return to its initial 66IT tBe rubs were mild enough to avoid permanent bow. However, this result does not have practical importance because we are only interested in the stability of the system at the starting of the rub. If the system is unstable, the resulting bow is so high that operation of the machine must be stopped to avoid major damage. 2 to 14 the followipa na;B0 static, initial bow of the rotor at the rubbing position, b dynamic vibration amplitude on a rotor fixed coordinate system, i phase angle between initial static bow and dynamic bow at time r， C radial clearance of the packing annulus，C phase angle between static and dynamic bow at time t.PARAMETER STUDYIn very complicated systems, when the solution depends on a large number of parameters, it is difficult to obtain general quantitative rules. In such cases，the laborious but rigorous approach is to go through the analysis and find the response of the system to the particular values of the input parameters.To investigate the parameters affecting the rubbing response, the calculationwqctpH frr cpvpra 1 rp cpc， (a) Effect of the dynamic parametersFor the numerical example considered here, it was found that the main factorwhich controls the rubbing stability of a system is the phase angle In Figs. 9，10 and 11 the response of the system at 1200, 1800, 3000 r.p.m” respectively，is plottedFig. 11 Newkirk Effect polar diagram-for several values of the phase angle. Generally, at = 0 the mode is always spiralling and at C = 7c the mode is always converging. Around the middle, at C = n/2 or ( = 37r/2, an oscillatory response is obtained. Based on these results, the chart in Fig. 12 was constructed. In areas where more than one mode overlap each other， the behaviour depends on the other parameters -of the system and the phase- angle alone cannot determine the mode characteristics of the system. This observation agrees with the test results and with an early observation of Taylor10, who noticed that at ranning speed above critical; light rubbing did not have any effect; When the rubbing force was increased，then the vibration amplitude became smaller.JV/ Efject ofthe generated heat and the geometry of the annul