Mathematical and physical simulation of diagnostics problem on the test rotor stand1)

Alexander I. Kumenko., Vladimir N.Kostukov, Ivan A. Suminov, Nikolay Y.Kuzminykh DYNAMICS SPC

Omsk, Omskaya Oblast, 644043,Russia, Tel: +73812-25-42-44

Fax: +73812-13-89 E-mail: 1949kai@mail.ru

Abstract

Some diagnostics problems of complex rotor systems for power turbine units are considered. A list of the main problems that must be solved for the diagnostics of technical condition of shafting on journal bearings is offered. One of the most difficult task – diagnostics of a residual deflection of separate rotors in the shaft line is also considered. The multiple-bearing test rotor stand with journal bearings for the analysis of physical processes and development of a number of diagnostic signs of the defects measured automatically with use of the shaft encoder complete system according to GOST P 55263-2012 is offered. The stand consisting of two rotors and a driving engine connected by rigid couplings allows to simulate and vary all main defects of production and assembly of rotors and bearings. The key geometrical and technical parameters of rotors are specified. The main dynamic characteristics of the rotor stand and results of simulation of a rotor deflection with use of the special software are provided. Key words: monitoring systems, automatic diagnostics, shaft encoders, turbine unit, shaft line, bearings, rotor deflection, amplitude, phase, critical speed. _______________________________________________________________________1) This work has been carried out with the financial support of the RSF according to Agreement No. 15-19-00267 dated 19 May, 2015.

1. About problems of diagnostics of complex rotor systems.

Today in the field of power stations a number of the practical diagnostic tasks directed to repair technologies and vibration adjustment has collected. For large turbine units it is not enough to use the spectral characteristics of stator elements and the results of their treatment. After assembly of a large turbine unit there is a set of residual defects which bring perturbations and impact the support spectral characteristics. Some defects, despite their size close to the limit, are poorly shown in vibration characteristics. So, for example, considerable misalignments of adjacent supports at good balancing and detuning of rotors from resonances may not prove in increased amplitudes of support vibrations, especially if supports are dynamically rigid [1]. At the same time, the resource of bolted connections of half-couplings is insufficient. Also, considerable misalignments of support can lead to lowering of rotor stability boundaries according to rotating speed, and small technological deviations in operation can cause surge of low frequency vibration, graze and damage of multiplexing or flowing part of rotors [2]. Therefore, the

range of tasks to evaluate technical condition of such machines extends. It is necessary to solve adjacent problems not always relating to vibration monitoring. 1.1 The list of the main objectives in the field of vibration diagnostics of turbine units The most important directions of rotor systems research by mathematical and physical modeling are the following: a) calculated and experimental study and analysis of physical processes and features of fluctuations at kinematic excitement in the conditions of operational misalignment, including: in the presence of residual rotors deflections and defects of rotors assembly on half-couplings in the wide range of rotation frequencies, the analysis of influence of support misalignment on forms of fluctuations and critical frequencies of the shaft line with the rotors having residual defects; b) specification of diagnostic signs and measurement of residual defects of the rotors assembly, including without its stop at a working rotation frequency; c) research and analysis of physical processes and features of fluctuations at various deviations of technological parameters at assembly of rotor systems; d) workout of a series of diagnostic signs of the defects measured automatically with use of full system of shaft encoders; e) working off of methods of high-precision balancing and diagnostics of rotors unbalances with use of full system of shaft encoder; e) comparison of the stand design characteristics to experimental ones; f) visualization of processes of the shaft movement at different types of defects; g) development of criteria for assessment of technical condition of rotor systems in use;. h) experimental check and workout of the solution of the inverse problem – definition under the values of rotors emersion of the correcting movements of support for correction of assembly and ensuring reliable work of coupling connections of the shaft line; i) use of methods of mathematical simulation for the solution of complex diagnostic problems in operation; j) specification of technical requirements to the systems of technical condition monitoring, including requirements to volumes and quality of measurements, etc. In one work it is impossible to consider all this volume list. We will stop on one group of the tasks connected with kinematic excitement of rotors in the shaft line. 1.2 About diagnosing of residual deflections of rotors One of the major diagnostic tasks not solved so far is an assessment of value and danger of origin or development in time of a rotor residual deflection. There is a lot of causes of residual deflection emergence [1], and recently this defect even more often appears at start-up because of low-quality repair. Therefore, tasks of assessment of a moderate residual deflection size without turbine stop, determination of the deflection point and the physical processes [1,4,5,9] happening at the same time are actual for monitoring systems development. The task of assessment of a deflection development in time is actual generally for high-temperature rotors of powerful turbines of 500 MW and more. Because of the creep phenomena residual deflection grows in them gradually and not directly or not always increases vibration on operating rotation frequency. The forms of residual deflections of flexible rotors often cause vibrations only on the first or third critical frequencies of

rotor. Around the operating frequency of rotation, work of forces arising in case of a deflection on relocation of rotors in the second vibration mode under certain conditions is small. As shown in [1], immediate causes of development of irreversible deflections in the conditions of creep are both unevenness of physical properties and unevenness of residual unbalances along a rotor axis. Besides, development even of a moderate initial deflection appeared due to any causes can continue because of action in the conditions of creep of both mentioned factors. A moderate residual deflection means a deflection which can be easily improved with necks pro-point and balancing. Usually, these deflections are up to 0,25-0,3 mm. At great values of a deflection, if there is no time for correction, special balancing under technology of LMZ [6,7] can be carried out as a temporary measure. But further such rotors have to go to repair with use of a special stand for rotor correction. For rotors which receive a moderate residual deflection a need arises in assessment of its value and place of origin for further assessment of technical condition and making further decisions. Also the dynamic behavior of a deflected rotor is of interest, both at start-up and in the zone of operating frequency with account for interaction with other rotors. Start-up of rotors with a residual deflection needs special additional requirements as the process of probable graze due to kinematic excitation is always unpredictable, a small deflection can turn into big with subsequent damage of the multiplexing or flowing part. Especially it is important for turbines which casing received residual deformations over time. Just a few researches are devoted to physical behavior of rotors with residual deflections. Attempts to replace kinematic excitation with the equivalent distribution of unbalanced masses [8] are incorrect, as it is shown in [9] a curvilinear rotor in the shaft line fluctuates with respect to the curved axis, and in all range of frequencies it is necessary to consider the kinematic offsets connected to a residual deflection. The requirements to values of rotors residual deflections and the requirement to radial and face flapping of a rotor separate parts, as a rule, are rigid [2,3]. According to the requirements to production and assembly of rotors stated in well-known textbooks, deflection value at the highest temperature of endurance at thermal test shouldn't exceed 0.05 mm (beating 0.1 mm). When checking on the lathe after thermal test deflection shouldn't exceed 0.025 mm. If in a cold state deflection makes up to 0.05 mm, it is allowed to bring it to the required value of 0.025 mm by necks pro-point. If deflection exceeds the specified value, the ingot axis and the forging axis don't coincide significantly, and the rotor is rejected; Thus, the limit value of beating according to the requirements of technological documentation makes 0.05 mm and any departure from these requirements involves risk of emergence of increased vibrations and, eventually, graze and increase in deflection. In regulating documents of manufacturers these values can slightly differ. Very often power plants save on repair of rotors, do not undertake necessary measures for deflection correction and use in work residual deflection rotors with beat to 0.3 mm and more. Thereby there are risks of more serious damage of a rotor at start-up, and considerable economic losses. Further we will consider some questions of mathematical and physical simulating of the vibration processes happening due to some defects in relation to rotors of the special experimental stand.

2 Mathematical and physical simulation of vibration processes of complex rotor systems

2.1 Mathematical models of vibration processes for solution of diagnostic tasks Over the last ecades the wide experience in solving many tasks for ensuring reliability of turbine units under designing has been accumulated. However, this experience is still used not enough for solution of diagnostic tasks in operation [3,4] and for vibroadjustment. Use of this experience and taking into account new opportunities of computer technologies allow to take a step forward not only in diagnosing and measurement of defects, but also in consequences of their influence, including for assessment of tension and a resource in elements of rotor systems. The specialists aspire it in both the power economy and aircraft industry [5]. Mathematical models for diagnostic tasks solution are based on linear ratios [5] and consider all main components and parameters of complex rotor systems, including:

− complexity and unevenness geometrical, inertial, stiffness and damping properties of rotors, bearings, support;

− aero and – hydrodynamic rigidity in sealing and flowing parts of turbines; − connectivity of support fluctuations ; − actual static loadings in support in operation and change of these loadings at

misalignment and external static impacts on rotors (cross aerodynamic forces in the control stage and in tail pipe in parts of high pressure;

− experimental data on dynamic pliability of supports of head turbine units; − physical properties of bearing lubricating fluids − physical properties of the turbine working substance, etc.

The main list of tasks for mathematical simulation of diagnostic criteria of technical condition and defects:

− kinematic excitement of rotors from residual deflections and assembling defects of rotors on half-couplings;

− dynamic excitement of rotor support with unbalanced masses and dynamic moments, support dynamic loads and residual unbalance of flexible rotors;

− static loads in supports and adjusting centering of rotors on half-couplings; − limits of dynamic stability of rotors according to rotation frequency and consumption

of steam in operation, etc.; 2.2 The main problems to be solved at the rotor stand The multisupport rotor stand with journal bearings is designed and manufactured for the analysis of physical processes, including for kinematic excitement in the conditions of operational misalignment, and workout of diagnostic signs of defects measured automatically with use of the full system of shaft encoders according to [11]. The physical model of the shaft line on journal bearings consists of two rotors of different length with 7 and 5 symmetrical masses. Two masses are located directly on the cross axis of 4 bearings (see fig. 1). Rotors are connected by a rigid coupling and driven through flexible communication by an electric motor of 10 kW. Shifts of rotors as regard to basic inserts are measured by 4 complete sets of sensors of the shaft relative vibration. Besides, additional systems of sensors measure movements of mass of rotors for workout of balancing problems and diagnostic of residual unbalance.

Single-component or three-component sensors of absolute vibration can be placed on supports according to GOST P 55265.2-2012. The system of rotors is designed so that rotors can have an expressed emersion curves, the lowest critical frequency can be about 1000 RPM for design value of rotating speed of 3000 RPM. The higher frequencies, due to possibility of their regulation, can be set as 2400 RPM and above. Each bearing is equipped with a complete system of sensors to record static and dynamic movements on both sides of each pins. Thus, for each pin system registers his radial and angular displacement, which then leads to movements in the vertical and horizontal planes. or rotation frequencies of base, including the operating speed must be pre-computed static and dynamic characteristics of the bearings. Fig. 2 shows the point on the curve of dynamic equilibrium that characterize the ascent rotors pins at the speed of 3000 rev / min. Ascent difference is not great, but it should be taken into account when assembling the rotors. The results of mathematical modeling of bearings will be tested and then used in the modeling of physical problems on the rotary stand. In addition, when the physical and mathematical modeling of problems of diagnostics will be used algorithms other several software packages: The software package EXVIB ('94 version, updated in 2016) allows us to simulate and get APFC, critical frequencies, forms of forced oscillations and trajectory for the 5 types of defects and their combinations [7], including: - The dynamic excitation of forced oscillations of a randomly distributed imbalances; - The dynamic excitement of randomly distributed points (for example, when a warp drives). - Kinematic excitation of axis fracture (for example, a pendulum-type coupling halves defect); - Cinematic thrill of the jump line of the shaft (eg, the type of coupling halves cranked defect); - Kinematic excitation of the residual deflection at rotor shaft lines; Also, any combination of these disturbances can be given.

1. Asynchronous electromotor, 3000 RPM 2. Half-coupling of EM 3. Piezoelectric vibrator 4. Eddy current sensor 5. Bearing support with an elliptic insert

6. Rotor No. 1 (mass of 35 kg) 7. Rotor No. 2 (mass of 22 kg) 8. Three-component vibration sensor 9. Incremental encoder (transformer of angular relocation) 10. Support of the rotor system

Fig.1 Model of the test rotor stand. Key parameters of the rotor stand are specified in the Table 1.

Table 1.

1 Parameter Rotor No. 1 Rotor No. 1 Note 2 Length Lр 1 m 0,5 m 3 Diameter of bearing

2R=D 60 mm 60 mm

4 L/D 1.167 1.167 5 Mass of rotor 35 kg 22 kg 6 Mass of disc 5.936 kg 5.936 kg 7. Lower critical

rotation frequency 12.42 Hz 31.16 Hz

8. Operating speed 3000 rpm 3000 rpm 9. Ellipticity of

bearing Var

10 Relative clearance Δб/R

0.005 0.005 Var

11 Limit misalignment of support 2-3.

Var

Fig. 2 The point on the curve of dynamic equilibrium shows difference between location of bearings pins #2 and #3 ( the degree of ellipticity m=0 ). Difference between location of bearing #3 and #2 0.006 mm in y direction and 0.009 mm in x direction (right increased).

The software package STRE21 ('94 version, upgraded and improved in 2016)

allows you to simulate and get shafting deflection line voltage in the rotor elements with misalignment of supports, path surfacing rotors necks when starting the turbine unit, shafting stiffness matrix of a single movements of supports.

It can also be used to solve the inverse problem (see section 1.1, paragraph "a" -... 'Experimental verification and testing of the inverse problem - determination on the values of ascent rotors corrective movements of supports to build correct and reliable operation of the coupling shaft line connections "). In addition, to evaluate resource bolting the coupling halves will be used by the mathematical model the bolts and bolts couplings [8], as well as regulatory materials [11,12].

3. Mathematical modeling of the "Rotor deflection" defect for the rotor stand

As an example we will consider modeling a residual deflection of a rotor of the experimental stand. The EXVIB program allows to set any form of a deflection with a series of sections (angular jumps of the shaft line, see fig. 3). At law rotations the rotor movement trajectory reproduces the required deflection to a high precision. Fig. 3 shows the projection in a vertical plane form of motion of the bent rotor on a phase through 20 degrees. The size of a residual deflection is about 60 microns.

In fig. 4 and 5 harmonic locus of an average point of the bent rotor in the vertical and horizontal direction for three options of unbalance are shown: П - a net deflection (unbalance is absent); Г - only the system of freights from a condition of approximate equality of amplitudes from a deflection and from freights at the first critical frequency for the horizontal plane is installed; Г+П (both freight and a deflection work at the same time. We will notice that the first critical frequency is split and for the horizontal plane it constitutes about 90 rad/s (860 rpm), and for vertical 120 rad/s or 1146 rpm. The compensating freights put to pass successfully the lowest critical frequencies. From fig. 4 and 5 it is well visible that without the compensating loads the deflection in the first form behind the first critical frequency is aligned and vibration aims at zero in case of rotating speed increase. If the compensating loads are set, then

the deflection on critical frequency for the horizontal plane is almost equal to residual and exceeds it by two and a half times on critical frequency for the vertical plane.

Fig. 3 Forms of a residual deflection for low rotations 10 rad/s (95,5 rev / min). Vertical projection.

Three options of indignation: Г-freight, П-deflection, Г+П freight and deflection. Horizontal projection.

Fig. 4 Amplitude-frequency characteristic of an average point of a rotor in all range of frequencies.

Amplitu

de,µ

m

Omega,rad/s

Amplitu

de,µ

m

Coordinate,m

Three options of indignation: Г-freight, П-deflection, Г+П freight and deflection. Vertical projection. Fig. 5 the Amplitude-frequency characteristic of an average point of a rotor in all range of

frequencies. Thus, in the presence of the compensating loads self-centering of a rotor between critical frequencies happens, but value of vibration practically remains at the level of a residual deflection. These calculations completely confirmed the outputs received by simulation of a deflection of medium-pressure rotor for shaft line by power unit 800 MW [4]. In fig. 6 projections of coupled modes in the vertical plane for a rotor in case of summary action of deflection and the compensating loads for rotating speeds from 10, 80, …. to 340 rad/s are shown. We see that on operating frequency of rotation the rotor with loads remains practically with the same deflection, as initial residual. It allows to draw important conclusions for the high-temperature rotors subject to creep and to define optimum system of the adjusting loads which will correct a deflection, but not to increase it according to [5,6] and confirms legitimacy of these operations.

Fig. 6 Forms of forced fluctuations of the bent rotor with compensation freights in all range of frequencies. Vertical projection.

Amplitu

de,µm

Amplitu

de,µm

Omega,rad/s

Coordinate,m

4. Conclusions

4.1 The main objectives in the field of vibration diagnostics and monitoring of technical condition of energy turbine units are formulated; 4.2 One of the most difficult tasks – diagnostics of a residual deflection of separate rotors in the shaft line is considered. 4.3 Mathematical and physical models of the shaft line for working off of diagnostic signs of defects and criteria of technical condition of complex rotor system with use of complete system of shaft encoder are offered. They use of in advance calculated charts of floating up of rotors journal 4.4 Results of mathematical modeling of dynamic characteristics of system of rotors in the presence of kinematic disturbance of one of rotors in the form of a residual deflection and the compensating system of freights are provided. 4.5 Physical processes and harmonic locus and vibration modes in broad range of frequencies of rotation are shown. Results of calculations show that, varying sizes of the compensating freights, it is possible to choose optimum system of freights for correction of a residual deflection of rotors in operation.

5. References

1. A I .Kumenko, V Yu Makhnov, M I Shklyarov,.. About the afterflow mechanism and possibility to correct the high and medium pressure rotors of powerful turbines by the balancing weights systems’/ Reliability and safety of power engineering, Moscow, 2009, № 4. 2. A I Kumenko., V N Kostyukov., N.Y Kuz’minykh., A.V Timin., G.V Bogdanov. Diagnostics of the shafting assembly while in operation with application of shaft sensors //Proceedings of the IV International Scientific Seminar on Advanced Assembly Methods on 22-23 October 2015, - Мoscow: Moscow State Machine-building University, - 2015. Pp.50-62. 3. A G Kostyuk, O A Volochovskaja. Evaluation of a two rotor vibration activity caused by curvature of its initial and residual imbalance, with freewheel.: Termal engineering, № 9. 2016. Pp. 12-18 4. A I Kumenko, O A Zlobin, I A. Suminov, I.A. Dynamic characteristics analysis, diagnostics and balancing of high temperature rotors having a permanent deflection // 10th International Conference on Condition Monitoring and Machinery Failure Prevention Technologies 2013, CM 2013 and MFPT 2013. 5. M I Shklyarov, N S Lebedko, A I Kumenko, ‘Recovery experience for rotors with permanent deflection’, Powerstations, Moscow, 2005, # 10. 6. M I Shklyarov, V G Kubarov, N N Shilovich, ‘Method of correction for steam and gas turbines rotors’, Patent 2079671 (Russian Federation). 7. E V Uriev, A V Kistoychev, A V Oleynikov, ‘Rotors correction by implementing the system of balancing and imbalancing weights’, Electrical stations, Moscow, 2009, № 1, pp 10-15. 8. A I Kumenko, I A. Suminov, O A Zlobin,., The dynamic characteristics of rotors with residual deflection // Proceedings of the VIII International scientific-practical conference "Improving the efficiency of energy equipment"Moscow.:, МPEI. 11-13 December, 2013 г. .

9. A I Kumenko, I A Suminov, I V Selifanov , G V Bogdanov. Diagnosis and prevention of residual deflection of the rotors in operation. // Problems of vibration, vibroadjustment, vibration monitoring and diagnostics of power plants equipment. / In papers. of VIII International Scientific-Technical Conference 17-19 November 2015, Moscow,: VTI. 2015 г. pp. 154-162. 10. A I Kumenko . Improving the experimentally-settlement methods of research of dynamic characteristics of turbine and its components. Diss. Doctor. tehn. sciences. Мoskow, МPEI, 1999 г. 11. GOST R 55263-2012 Vibration. "Evaluation of machine vibration by measurements on rotating shafts". Part 2: Stationary steam turbines and generators over 50 MW with an operating frequency of rotation of 1500, 1800, 3000, 3600 rev / min. - M .: Standartinform, 2014 - 12. 12. A I Kumenko, ‘Comprehensive analysis of the vibration reliability turbosets’, The 7th International Conference on Condition Monitoring & Machinery Failure Prevention Technologies, CM 2010/MFPT2010/ 22-24 June, 2010, Stratford-upon-Avon, England, BINDT&Coxmoor Publishing Co., ISBN: 978-1-901892-33-8, 2010, Paper 240, 20 p.

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Session 3A – Maintenance and machinery simulation Chair: Professor V Kostyukov and Professor A Kumenko Room: Decouverte 3 and 4

15.50 [139] Mathematical and physical simulation of diagnostics problem on the test rotor stand

Author - A I Kumenko, V N Kostyukov, I A Suminov and N Y Kuzminykh, Dynamics SPC

Some diagnostics problems of complex rotor systems for power turbine units are considered. A list of the main problems that must be solved for the diagnostics of technical condition of shafting on journal bearings is offered.Oneofthemostdifficulttask–diagnosticsofaresidualdeflectionofseparaterotorsintheshaftlineis also considered.The multiple-bearing test rotor stand with journal bearings for the analysis of physical processes and development of a number of diagnostic signs of the defects measured automatically with use of the shaft encoder complete system according to GOST P 55263-2012 is offered.The stand consisting of two rotors and a driving engine connected by rigid couplings allows to simulate and vary all main defects of production and assembly of rotors and bearings. The key geometrical and technical parametersofrotorsarespecified.Themaindynamiccharacteristicsoftherotorstandandresultsofsimulationofarotordeflectionwithuseofthe special software are provided.

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