Esnek rotorlarda dengeleme probleminin incelenmesi
The Analysis of the balancing problem in flexible rotors
- Tez No: 35131
- Danışmanlar: PROF.DR. H. TEMEL BELEK
- Tez Türü: Yüksek Lisans
- Konular: Makine Mühendisliği, Mechanical Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1994
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 107
Özet
ÖZET ESNEK ROTORLARDA DENGELEME PROBLEMİNİN İNCELENMESİ Bu çalışmada, endüstride geniş bir kullanım alanına sahip olan dönel makinalarm (rotorlar) yerinde dengelenmesine yönelik araştırmalar teorik ve deneysel olarak incelenmiştir. Bu maksatla öncelikle dönel makinalar ve bu makinalarm yerinde dengelenmesini sağlayacak yöntemlerin başlıcalan olan Modal Dengeleme ve Tesir Katsayıları ile Dengeleme yöntemleri tanıtılmış, daha sonra her iki yöntemin avantajlarını birleştirirken dezavantajlarını elimine eden ve son gelişmiş yöntem olan Birleşik Dengeleme Yaklaşımı adı verilen yöntemin anlatılmasına geçilmiştir. BDY ve tesir katsayıları ile dengeleme yöntemlerinin gerçek rotorlar üzerinde nasıl sonuçlar vereceğini görebilmek maksadıyla bir deney düzeneği kurulmuş ve elde edilen sonuçların başarılı bir dengeleme için yeterli olup olmadığı incelenmiştir. Bu yöntemlerin gerçek bir rotora uygulanması sırasında, mil-disk sisteminin boyutlandırılabilmesi maksadıyla kritik hızların ve mod şekillerinin hesaplanması gerekli olduğu için, bu değerleri veren ve elde mevcut olan bir bilgisayar programı çalışmamıza uygun olarak konfigüre edilmiştir. Dengeleme işlemine geçildiğinde ise, her iki yöntemin de işleyiş prosedürünü adım adım izleyen, ölçülen titreşim değerlerini giriş datalan olarak alan ve sonuçların elde edilmesini sağlayan birer bilgisayar programı hazırlanmıştır, özellikle BDY yönteminin oldukça karmaşık işlemler içermesi ve yöntemi uygulayacak olan operatörün adımlardan herhangi birini atlaması ya da yanlış uygulaması ile istenilen sonuçlara ulaşılamayacağı için, pratikte bu programı kullanacak olanlara kolaylık sağlamak maksadı ile, programda her adımdaki işlemler ve gerekli uyanlar diyaloglar yoluyla ekrana yazdınlmıştır. Uygulamalar sırasında ise elde mevcut motorla istediğimiz kritik hızlara çıkılamadığı ve mil uzunluğu deney tesisatı sebebiyle sınırlandırıldığı için, BDY yönteminin test edilmesi uzun uğraşlara rağmen mümkün olmamış, sadece Tesir Katsayılar Yöntemi test edilebilmiştir.
Özet (Çeviri)
SUMMARY THE ANALYSIS OF THE BALANCING PROBLEM IN FLEXIBLE ROTORS The mass balancing of rotating machines (referred to more briefly as rotor balancing) has been an important consideration in machinery design and manufacture for more than forty years. Reduction in weight, coupled with increased operating speeds, have substantially increased the flexibility of rotating machinery. Also, many types of machines are currently being designed to operate supercritically, and this trend is likely to continue. Consequently, reduction of mass unbalance in rotating machinery is often essential to ensure safe operation and reasonable life for such machines. The unbalance in the rotors will not only cause vibrations, but also transmit rotating forces to the bearings and to the foundation structure. The forces thus transmitted may cause damage to the machine parts and its foundation. In some cases, if the transmitted force is large enough, it might affect even the neighbouring machines and structures. For this reason, it is necessary to remove the unbalance of a rotor for its smooth runnings by adding or removing calculated correction masses. The location where the correction mass is to be added or removed can be determined simply by an experiment of statics if the rotor has only one disk or the balancing is required in one plane. Such a process is called static balancing. If the unbalance is distibuted along the length of the rotor, as it is in many cases, then a static balancing procedure cannot be used to determine the correction masses. This is because the centre of gravity of the rotor may be brought to the centre line of the shaft, but there could be an unbalanced moment left in the rotor, generating equal and opposite rotating reactions. This unbalance can be removed by dynamic tests only and hence called dynamic unbalance. This procedure is simple if the rotor is ideal or rigid. In this study rigid rotor balancing methods are studied in some detail for knowledge. If the shaft uerîects and the deflection changes with speed, as it does in the vicinity of the critical speeds, the problem of balancing is complicated. In this case, these rotors need special flexible rotor balancing procedures. Consequently, rotor balancing procedures are classified according to the type of rotor for which they are designed, rigid or flexible. When rigid rotors are balanced, the shape of the centroidal axis as a function of speed does not change. For flexible rotors, the shape of the centroidal axis, and thus the unbalance distribution, does change with speed. In general, rigid rotor balancing procedures and tools are not applicable to the balancing of flexible rotors. However, the same is not true for the current flexible rotor balancing procedures. These procedures can be classified into two groups, modal balancing and influence coefficient balancing. In the past, these two general balancing methods have competed, each with the inherent advantages and disadvantages of the other. In both cases, the disadvantages have been significant enough to prevent widespread acceptance of the balancing procedure. Consequently, most flexible rotor balancing is currently done by trial and error procedures, which are inefficient. In this study, a unified approach to the balancing of flexible rotors [1] which bridges the gap between modal and influence coefficient balancing is described. This 11new balancing method (hereafter referred to as the Unified Balancing Approach) combines the advantages of modal and influence coefficient balancing and eliminates the disadvantages of the two current procedures. At the same time, the Unified Balancing Approach provides a straightforward, practical approach to flexible rotor balancing, is well-suited to both production and field balancing. Briefly,the influence coefficient method seeks those correction masses in a predetermined set of planes which will minimize measured vibration (readings) at a series of sensors and speeds as predicted by influence coeffîcients,relating reading to mass additions.The influence coefficients are normally determined by a series of trial mass tests. The modal method seeks to balance the rotor,one mode at a time, with a set of masses specifically selected to leave previously balanced lower modes undisturbed. Sensitivity to this combination of masses as a set is determined empirically by a series of trial mass tests. Specific advantages and disadvantages, identified with each method,take on different relative importance according to the requirements of a particular balancing process.The only trial mass runs that are required at the highest balancing speed involve the combined weight sets for modal response. Individual trial mass runs are not required. Since, by design, the lower modes are not affected by a modal trial mass set, this mass set can be made large enough to assure good sensitivity at the mode being balanced. Eliminating the danger of upsetting the condition of previously balanced modes generally simplifies the balancing of higher modes. Only a basic understanding of the dynamics of the rotor system is needed to select locations for vibration sensors and balancing planes. It is not necessary to have prior knowledge of the system. Modal balancing does, of course, assume that the responsee of the rotor system is linear and that the vibration sensors are sufficiently accurate. Modal balancing sometimes requires analytical procedures for selecting the sets of trial masses used for correcting spesific modes. Not only does the requirement for this analysis complicate the balancing procedure but any inaccuracies in this analytical model reduce the effectiveness of the balancing procedure. Analytical procedures are not necessary, however, and several proponents of modal balancing employ emprical procedures to determine the modal trial mass sets. This emprical procedure has disadvantages, also. It requires substantial operator insight into the modal character of the whirl of a rotor due to unbalance, and this requirement inhibits the efficiency of production balancing techniques. Balancing a rotor to eliminate vibration as measured by a single sensor may not result in minimum vibration for the rotor as a whole, particularly when mode shapes are distorted or non-planar. Difficult may also occur as a result of vibration from other modes not previously balanced. Methods have been developed to correct this problem [7], but once again operator insight is required. As for the influence coefficient balancing : influence coefficient balancing is an entirely emprical procedure, its effectiveness limited only by the linearity of the rotor system and the resolution of the vibration sensors. Only a minimum knowledge of the rotor system is required for specifying the locations of the vibration sensors and balancing planes (for the application of correction masses). Influence coefficient balancing provides for the simultaneous balancing of more than one mode, provided that the necessary sensitivity information (influence coefficients) is available. This feature can reduce the required number of balancing runs but does require measurement of the rotor vibration at speeds near the relevant critical speeds. It may innot be safe to ruri through öne of these critical speeds to make measurements at higher speeds. The emprical nature of this procedure and the modest skills required of the operatör, along with the required calculation form, make this procedure ideally suited for computerizing and automating. Least-squares minimization of vibration data allows for balancing criteria, based on reducing the vibration for a number of points in the rotor system and for any number of modes. This feature of influence coefficient balancing can often be used to compensate for distorted ör non-planar mode shapes and the effect of other unbalanced modes. Additional data manipulation techniques, designed to compansate for measurement errors inherent in any realistic application of rotor balancing are available. Since individual trial mass runs must be made at the highest balancing speed when using influence coefficient balancing, the total number of runs required for this speeds may be limited by the response of lightly damped lower modes to these trial masses. The initial unbalance preseni for the higher modes may make it impossible to acquire sensitivity data, using a restricted trial mass, at a speed clo.se enough to a higher critical speed to produce a significant effect from this trial mass. That is, if the largest possible trial mass is small compared to the initial unbalance at the higher mode, the resolution of the sensitivity data acquired for this trial mass may be substantially reduced. When a particular mode is balanced after a number of other modes have been balanced, a large quantity of data may be required. This requirement can affect the accuracy and convenience of the balancing procedure. Due to their inherent disadvantages, neither modal nor influence coefficient balancing has gained widespread acceptance. Consequently, most practical flexible rotor balancing uses öne of a number of trial and error procedures which are generally inefficient and often ineffective. The Unifîcd Balancing Approach (UBA) is intended to incorporate the advantages of both the influence coefficient and modal balancing methods, while eliminating the disadvantages of both methods. That is, the Unified Balancing Approach uses a modal method of applying correction masses in modal sets using data derived in an emprical manner and requiring a minimum of prior knowledge of the dynamics of the rotor. Essentially, the technique involves the calculation of modal trial mass sets based on the computerized influence coefficient procedure of taking trial mass data. Generally, these modal trial mass setş are determined in such a way as to affect the mode of interest while not affecting the lower modes that have already been balanced. Hovvever, if appropriate data are available from previous tests ör from numerical predictions, a modal trial mass set can be conducted that will have no effect on any general set of modes. in general, the number of planes required for the modal trial mass set is öne more than the number of modes which must not be affected. The procedure for applying the UBA is described below and also illustrated in the flowchart in section 3.2.2. to give a clearer understanding of the process. This approach is designed to handle a number non-ideal (but not uncommon) conditions, including the occurrence of non-planar ör distorted mode shapes and the existence of measurement error and fmite vibration data resolution. A computer program is generally required to perform the necessary calculations. ivl Thc hasic proccdurc lor implcmcnting tlıc UBA is as follovvs: 1.The balancing specifıcations for the rotor system are defined. These specifıcations include the number, types (e.g., displacement, velocity, acceleration ör force) and calibration factors of the vibration sensors to be used and the specifıc sensors vvhich are most sensitive for each of the modes to be balanced; the number of balancing planes and balancing mass holes specifıcations for each plane, as well as the specifıc planes vvhich comprise each of the modal trial mass sets; the angular location of the trial masses and vvhether additional trial mass runs for reduction of measıırement errors are to be used; the numbeer of modes to be balanced and the speed at which vibration data are to be taken for each mode (these values may be changed by the operatör during the balancing procedure, if necessar). This is the only step in this balancing procedure which requires engineering-level decisions to be made. The remaihder of the steps may be handled by a skilled operatör. Thus this balancing procedure is well suited for application to production balancing, where step öne needs to be done only önce. 2.Thc rotor is run at a vcry slow spccd (to cnsure that no dynamic response is preseni), and rendings nro inken from displncement mensııring sensors only. These readings are referred to as static runout data and are due to rotor surface eccentricity and other sources of synchronous data, such as an initial bend in the rotor, vvhich are not caused by rotor mass unbalance. in general, this static runout data is independent of the rotational speed of the rotor. The true vibratory response of the rotor at other rotational speeds is found by subtracting the static runout from the measured vibration readings. If none of the sensors measure rotor displacement, this step may be by- passed. 3.The undisturbed rotor (no trial masses installed) is run, and vibration readings are taken for the mode to be balanced and for ali modes which are not to be affected by the balancing procedure, at corresponding specifıed speeds. If previously measured modal influence coefficients are available for the mode to be balanced, the balancing procedure is continued with step 6. If this is not case, but there are no uneffected modes (vvhich is usually the case when balancing the fırst rotor mode), the balancing procedure is continued with step 5. Othenvise, step 4 follovvs. 4.Individıml irial masses are installed in each of the planes to be used for balancing the mode of interest (öne at a time), and vibration readings are taken at the specifıed data speed for each of the unaffected modes. If reciprocity is used, only öne balancing plane is used here. Either öne ör two trial masses are used for each balancing plane, as specifıed in step 1. The complex modal trial mass ratios (the vector rw) are then calculated. 5.A modal trial mass set is installed (vvhich consists of a single mass, if there are no unefTeclcd modes), and vibration readings are taken at the specifled data speed for the mode to be balanced. A seeond modal Iriııl mass sel is instnlled and another set of vibration readings are taken, if so specifıed in step öne. The modal influence coefficients for the mode being balanced are then calculated, based on this modal trial mass data and the uncorrected rotor data from step 3. v6. The modal correction mass set is calculated for the mode being balanced, based on the modal influence coefficients and' the uncorrected rotor data from step 3. The operator then installs this modal correction mass set. 7. Another set of vibration readings is taken at the specified data speed for the mode being balanced to determine whether sufficient improvement of the rotor response has been achieved by this balancing procedure. The measured residual vibration is either displayed to the operator, for the. operator to evaluate, or is compared to perviously specified balancing criteria (from step 1.) If the measured residual vibration is determined to be acceptable, the balancing procedure is continued with step 9; otherwise step 8 follows, i 8. If additional improvement in the measured residual vibration is required, and if it is determined that this improvement can be achieved using the same balancing speed (using the same modal influence coefficients), the balancing procedure is continued with step 6. If, however, it is determined that a more sensitive balancing speed (nearer to the critical speed) is required, or that updated modal influence coefficients are needed (due to non-linearity in the rotor system), the balancing procedure is continued with step 5. A balancing speed nearer to the relevant critical value may also be required to isolate the mode being balanced from other modes.9. If one or more modes remain to be balanced, the mode just balanced is added to the list of unaffected modes; the next mode to be balanced is chosen, and the balancing procedure continues with step 3. 9. If one or more modes remain to be balanced, the mod just balanced is added to list of uneffected modes; the next mode to be balanced is choosen (as specified in step 1), and the balancing procedure continues with step 3. 1 0. After the last mode has been balanced, the modal influence coefficients which have been measured may be stored for later use in rebalancing the same rotor or in balancing other rotors of the same type. This completes the balancing procedure for this rotor. It should be noted that, when using measured modal influence coefficients to apply. to a class of rotors, it may be necessary to measure the modal influence coefficients for several of these rotors and statistically average these values to get a set of modal influence coefficients which can be applied with good results to a whole class of rotors. As indicated above, the UBA inherently avoids the principal disadvantages of both modal and influence coefficient balancing. However, there is a cost associated with these improvements. The UBA has some apparent advantages over both modal and influence coefficient balancing, as follows 1. No prior knowledge of the modes of vibration of the rotor to be balanced is required. The necessary information is determined emprically in the course of balancing. It is helpful if the critical speeds are known approximately. VI2. As with modal balancing, the modes can be balanced individually, while not affecting the balance of other modes that have already been balanced. 3. In particular cases where the lower modes are more lightly damped than the highter modes, the use of modal trial mass sets allows the application of substantial trial masses at the insensitive modes, while not aggravating the response of the lower modes. It should be noted that individual trial mass runs that are required for the UBA always involve modes that have already been balanced. Therefore, the vibration readings for these individual trial mass runs can always be taken at speeds close to the critical speeds so that small trial masses can be used with substantial effect, while the rotor is not prevented from going through lower critical speeds. 4 Using the UBA, a smaller number of runs is required at the highest speeds of the rotor than would be required for influence coefficient balancing with individual trial mass runs. For rotors which obey the prinnciple of reciprocity, and for which closely adjecent planes and sensors are available, the total number of individual trial mass runs can also be substantially reduced ( as discussed below ). 5. In many cases, the balancing of a particular mode begins well below the corresponding critical speed, and the response at the balancing speed is reduced to the point where, even though no additional improvement can be made (because of limited vibration pickup sensitivity), the critical speed can still not be negotiated. Using the Unified Balancing Approach, only a single trial mass run is required at the higher balancing speed. However, using influence coefficient balancing, a complete new set of trial mass runs is required at the higher speed. Thus, use of the Unified Balancing Approach substantially reduces the number of balancing runs. 6. Production balancing of a series of idendical rotors can be greatly simplified through the use of emprically determined and statistically avaraged standard modal influence coefficients. The trial mass runs become small or even nonexistence. In this study, the three principal flexible rotor balancing methods: modal balancing, influence coefficient balancing and the Unified Balancing Approach are described. Each of these methods is discussed in some detail, including analytical basis and specific implementation procedures. Then, for UBA and for influence coefficient balancing, computer programs are prepared. The program for influence coefficient balancing is applied on an experimental set-up for 4 measurement points and 3 correction planes using the influence coefficient balancing procedures, and then results are discussed in the last section. Vll
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