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Shaft instantaneous angular speed for blade vibration in rotating machine
Mechanical Systems and Signal Processing ] (]]]]) ]]]–]]]
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Shaft instantaneous angular speed for blade vibration in rotating machine Ahmed A. Gubran, Jyoti K. Sinha n School of Mechanical, Aerospace and Civil Engineering (MACE), The University of Manchester, Sackville Street, Manchester M13 9PL, UK
a r t i c l e i n f o
abstract
Article history: Received 29 June 2012 Received in revised form 19 December 2012 Accepted 3 February 2013
Reliable blade health monitoring (BHM) in rotating machines like steam turbines and gas turbines, is a topic of research since decades to reduce machine down time, maintenance costs and to maintain the overall safety. Transverse blade vibration is often transmitted to the shaft as torsional vibration. The shaft instantaneous angular speed (IAS) is nothing but the representing the shaft torsional vibration. Hence the shaft IAS has been extracted from the measured encoder data during machine run-up to understand the blade vibration and to explore the possibility of reliable assessment of blade health. A number of experiments on an experimental rig with a bladed disk were conducted with healthy but mistuned blades and with different faults simulation in the blades. The measured shaft torsional vibration shows a distinct difference between the healthy and the faulty blade conditions. Hence, the observations are useful for the BHM in future. The paper presents the experimental setup, simulation of blade faults, experiments conducted, observations and results. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Instantaneous angular speed (IAS) Blade vibration Blade health monitoring (BHM) Blade faults Shaft torsional vibration Order tracking
1. Introduction Rotating blades are considered as the most common cause of failures in rotating machinery. The blade failure modes normally occur as a result of cracking, high cycle stresses, blade rubbing, blade root looseness, degradation from erosion and corrosion. Therefore, early fault detection is important in reducing blade related failures and hence there is a need of a reliable and simple blade health monitoring (BHM) technique. Sinha et al. [1] recently analyse the in-situ measured vibration data at the bearing pedestals during the steady state and the transient operations in the steam turbines to understand the machine dynamics, and to identify the root cause of the failure of the last stage blades in the low pressure turbines. Al-Bedoor [2] gave the review of different research methods that has been attempted for blade vibration measurements till year 2002. In-situ casing vibration near the last stage of a low pressure (LP) turbine in a steam turbogenerator (TG) set was observed to show the trace of blade resonance only during the fluctuation in the condenser pressure due to change in loads [3]. But such observation contains very limited information and may not be useful for diagnosis. Strain measurement on the blades during the machine operation is another option [4], this is where strain can be measured directly and hence the stress and possibly residual blade life can be estimated [5]. The blade tip time (BTT) has received attention in recent years and it can identify blades with high vibration [4,6]. However both the BTT and the strain measurement methods are intrusive and exorbitant methods. Hence there is a need for reliable and simple but robust method to meet the requirements of the BHM.
n
Corresponding author. Tel.: þ44 161 3064639; fax: þ 44 161 3064601. E-mail addresses: [email protected], [email protected] (A.A. Gubran), [email protected] (J.K. Sinha).
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Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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A.A. Gubran, J.K. Sinha / Mechanical Systems and Signal Processing ] (]]]]) ]]]–]]]
The use of the encoder in rotating machines is seems to be a common practice to measure the shaft speed. The shaft instantaneous angular speed (IAS) signal from the encoder raw signal based on time-intervals change between successive pulses is nothing but the representing the shaft torsional vibration. This method is generally non-intrusive and nonexorbitant method and now the topic of research for different applications. A few of them include the identification of faulty combustion cylinder(s) in the diesel engines [7,8] using the crank shaft IAS signal and the IAS response of the shaft with fault(s) in rotating machine [9,10]. It has also been reported in the literature that transverse blade vibration is often reflected in the shaft torsional vibration. It was experimentally verified on small rigs, and the mistuning effect on the blade natural frequency was also observed [11,12]. Maynard and Trethewey [13] have also demonstrated the field application on the use of the torsional vibration for tracking crack in shaft and blades. Analytical simulations [14] and Huang and Ho [15] have also shown the potential of the shaft torsional vibration that could be used as the condition monitoring for turbine blades. However, Sinha et al. [16] could not identify the last stage blade resonance during normal operation of a steam turbine in a 220 MW Nuclear Power Plant in India. The transient operation of machine may be useful for such machines. Hence the shaft IAS has been extracted from the measured encoder data during the machine transient operation to understand the dynamics of the blades and to explore the possibility of reliable assessment of the blade health. A series of experiments were conducted on a test rig with an 8-bladed disc for three different conditions: (1) healthy with mistuned effects, (2) blade root looseness and (3) blade(s) with crack. These conditions are often observed in practice for the rotating machines like steam turbines, gas turbines, etc. and hence the early and reliable detection of the faulty conditions (2) and (3) is important. The extracted IAS signal from the encoder raw data during the machine run-up were then order tracked at the different engine order (EO) speeds so that the presence of the blade resonances, their higher harmonics and dynamics behaviour can be analysed. The measured shaft torsional vibration shows a distinct difference between the healthy and the faulty blade conditions and hence the observations may be useful for the BHM in future. The paper presents the IAS extraction process from the encoder measurement, rig details, blade faults simulations, experiments conducted and the observations on the blade dynamics which may possibly lead to the BHM in future.
2. Instantaneous angular speed (IAS) measurement An encoder that measures 360 pulses for every complete rotation of a shaft has been used for the present experiment. To aid the understanding of the IAS signal extraction from the measured encoder pulse train, a simplified measurement scheme of the encoder and the pulse train is shown in Fig. 1. The sensor simply measures the gap between each tooth on the gear during its rotation which results in the pulse train of the measured gap voltage with time as shown in Fig. 1. The extraction of instantaneous angular speed (IAS) signal using the pulse train in Fig. 1 is discussed in the following steps. (i) Each square pulse represents a tooth in the gear of the encoder, hence the difference of times, t 2 t 1 , t 3 t 2 , y.,t n þ 1 t n , etc. represents the time interval required to cross the 1st, 2nd, y., nth tooth respectively which is written as
Dtn ¼ tn1 tn
ð1Þ
Fig. 1. Pulse train created from shaft encoder.
Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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It is also assumed that the time interval for nth tooth is measured at the time, T n as Tn ¼
tn þ tn þ 1 2
ð2Þ
where n¼1, 2, 3, 4, 5,y, N number of teeth in the gear of the encoder. (ii) The angular displacement Dy for the each equally spaced tooth in the gear wheel of the encoder can be written as
Dy ¼ 3601=N ¼
2p N
ð3Þ
(iii) Hence the instantaneous angular speed (IAS) at time, T n in terms of revolution per second (RPS) can be calculated as Instantaneous angular speed ðIASÞ ðf sn Þ at ðT n Þ ¼
Dy ðDt n 2pÞ
ð4Þ
The extracted IAS signal from the measured pulse train from an encoder may look as shown in Fig. 2 if the shaft is rotating at a constant speed. It is expected to be the ideal case when there is no fluctuation in the speed during the shaft rotation and/or no shaft torisonal vibration i.e., Dt 1 ¼ Dt 2 ¼ Dt 3 ¼ ¼ Dt N . However in reality these time intervals, Dt n , may not be always constant due to the speed fluctuation and/or due to the presence of shaft torsional vibration and can be presented as Fig. 3. The time vectors, T n and corresponding IAS, f ns may not be at the equal time interval, hence the data are re-sampled with a uniform time interval before further signal processing. 3. Experimental setup In order to investigate the feasibility of torsional vibration measurement technology for incipient blade deterioration, an experimental test rig was built in the dynamics Lab at the school of MACE at the University of Manchester for this study. The test rig mainly consists of: (a) 1 hp 3-phase motor, (b) two SKF type YS 20 TF, ball bearings, (c) a steel shaft of diameter 20 mm, (d) a bladed disc with eight rectangular blades, and (e) a flexible coupling between the motor shaft and the rotating rig shaft. The schematic of rig with the instruments is shown in Fig. 4. A photograph of the test rig including the measurement system is also shown in Fig. 5. The dimensions and material properties for the shaft–disc–blade system are listed in Table 1. The photographs for a blade and a bladed disc are also shown in Fig. 6. 3.1. Instrumentations Figs. 4 and 5 also show the mounting of the encoder at the end of the rotor shaft and the accelerometers on the bearing housing. The measuring system composed of one rotary shaft encoder, Kubler-2400, which generate 360 pulses per revolution. A tacho sensor (Model S51-PA-2-A00-NK) retro-reflective optical sensor was used to monitor rotating speed.
Fig. 2. Idealised shaft IAS showing constant shaft speed without torsion.
Fig. 3. Typical shaft IAS showing the possibility of the shaft torsion.
Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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Fig. 4. Schematic of the test rig with instrumentations.
Fig. 5. Photograph of the test rig.
Table 1 Shaft–disk–blades data. Part
Property
Value
Shaft
Material Length Diameter
Stainless steel (E ¼210 GPa, r ¼ 7800 kg/m3) 600 mm 20 mm
Disc
Material Width Outer diameter, Do Inner diameter, Di
Steel (E ¼210 GPa, r ¼7800 kg/m3) 20 mm 50 mm 20 mm
Blade (8 numbers)
Material Length Width Thickness
Steel (E ¼210 GPa, r ¼7800 kg/m3) 110 mm 20 mm 2 mm
The output of the encoder and the tacho sensors are connected to the data acquisition board NI USB-6221 for data collection and storage into the PC. The photograph of the data acquisition board with PC is shown in Fig. 7.
4. Modal testing Modal testing has been conducted on the test rig for the eight blades in order to determine blade natural frequencies by using the Impulse-Response modal test [17]. Each blade was excited using an instrumented hammer (type PCB-0860C03) and the vibration responses were measured using a tiny accelerometer (Model 352C22, M/s PCB) weighing just 0.5 g. The blades natural frequencies were identified using the frequency response functions (FRF) calculated from the measured Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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Fig. 6. (a) A blade and (b) bladed disc.
Fig. 7. Rig measurement systems.
force and acceleration data. The experimentally identified first natural frequency for each blade is listed in Table 2. A small deviation in blade natural frequencies showing the presence of the blade mistuned effect due to possibly small deviation in blade manufacturing and/or fitting.
5. Faults simulation and experiments Three different blade faults were simulated for the experiments. These conditions of blade are: (a) Case 1: Healthy blades with mistuned effects, (b) Case 2: Blade root looseness and (c) Case 3: Crack on blade(s). These are summarised in Table 3 and also discussed in the following sections. Fig. 8 illustrates the faulty blade(s) position with respect to the tacho sensor location. Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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A.A. Gubran, J.K. Sinha / Mechanical Systems and Signal Processing ] (]]]]) ]]]–]]]
Table 2 Experimentally identified blades 1st natural frequency. Blade no.
Blade 1st natural frequencies (Hz)
1 2 3 4 5 6 7 8
123.75 126.25 125.00 127.50 128.75 123.75 125.00 125.00
Mean frequency (7 deviation)
125.625 (7 3.125)
Table 3 Blade faults conditions. Case
Description
Blade no.
1
Healthy with mistuned
–
2
Blade root looseness
(i) Blade no. 1 (ii) Blade no. 5
3
Crack on blade(s)
(i) Blade nos. 2 and 4 (two cracked blades together) (ii) Blade no. 2, 37 mm from blade root (iii) Blade no. 4, 22 mm from blade root (iv) Blade no. 4, 22 mm from blade root, after 100 min of machine operation
5.1. Healthy blade with mistuned effect The healthy blade with mistuned case (Case 1 as per Table 3) for the blades is tested initially where the variation in the 1st natural frequencies is listed in Table 2. It is the most likely condition of the healthy blades in any rotating machines like the steam turbines, gas turbines, etc.
5.2. Blade root looseness If the blades are not properly mounted and assembled on the shaft disc then the blades root may be loose that could result in rubbing during machine operation which may lead to the failure. Hence this root looseness fault is simulated by putting 2 free loose washers on the root of Blades 1 and 5 separately as per the Case 2(i) and Case 2(ii) in Table 3. Fig. 9 shows the root looseness simulation.
5.3. Blade crack simulation A small cut on blade of 0.6 mm width by a thin saw was made on 2 blades but at different locations. A very thin metal sheet placed on blade cut using adhesive glue from one side of cut so that breathing (opening and closing) of crack in the blade can be realized during vibration. The crack made on the 2 blades is shown in Fig. 10 and the cracked blades in the rig in Fig. 11. Here, a total of 4 tests were conducted for the cracked blade case as per Table 3 to understand the dynamic behaviour of crack blade(s) in different combinations; crack in a single blade but different location, crack in 2 blades simultaneously and the impact on the dynamic behaviour when a crack blade, Case 3(iv), is tested after 100 min of machine operation.
5.4. Experiments conducted The vibration experiments have been carried out for all cases listed in Table 3 (i.e., Healthy, Root looseness and Crack blade). Initially the experiments were conducted at different constant shaft speeds but the excitation of the shaft torisonal vibration was not observed to be significant, hence the further experiments were conduced during the machine run-up from 600 rpm (10 Hz) to 1800 rpm (30 Hz). The run-up rate was kept equal to 40 rpm/s. The measured analogue signals by the encoder and tacho sensors were then collected at 50,000 Samples/s and stored into the PC for the further signal processing. Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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7 (270°) 6 (225°)
8 (315°)
5 (180°)
1 (0°)
4 (135°)
2 (45°) 3 (90°)
Fig. 8. Schematic diagram of the blade positions with respect to the tacho sensor.
Fig. 9. Simulation of blade root looseness fault: (a) Blade 1 and (b) Blade 5.
Fig. 10. Blade crack simulations: (a) front side of a crack, (b) back side of a crack, (c) a very thin metal sheet in the crack, (d) crack locations 37 mm and 22 mm from blade root for Blades 2 and 4 respectively.
Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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Fig. 11. Different view of a typical cracked blade on the bladed disc in the rig.
Fig. 12. A typical rotor speed profile for the rig during run-up.
Fig. 13. A typical measured encoder signal.
6. Data analysis The measured tacho sensor and encoder data were analysed for all the cases to extract the shaft speed with time and the IAS signal with time as suggested in Section 2. A typical shaft speed from the tacho sensor and the raw signal from the encoder for the healthy blades condition (Case 1) are shown in Figs. 12 and 13 respectively. The extracted IAS signals are then processed with the different engine order (EO) speeds to understand the appearance of blade resonances, their higher harmonics and dynamics behaviour. It has been observed that the EO5 and its higher harmonics (EO10, EO15, y) contains the blade responses in the IAS signals. Fig. 14 shows a typical EO5 response for Case 1 healthy condition. The peak around 94 Hz and 108 Hz are related with the shaft torisonal resonance (with the flexible coupling to the motor) and the critical speed of the rig (the rig natural frequency). A hump around 120–130 Hz is related to the blade resonance (BR) region indicates that the blades are excited during the machine run-up and related in a banded resonance due to the blade mistuning. Fig. 15(a) shows the zoom view of Fig. 14 in the frequency range 120–135 Hz so that blade response in the resonance region can be clearly observed. The EO5 responses in the BR in the frequency band of 120–135 Hz for Cases 2 Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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Fig. 14. A typical IAS response at EO5 for Case 1: Healthy blade.
Fig. 15. Typical IAS responses at EO5: (a) Case 1: Healthy, (b) Case 2(i): Blade 1 looseness, (c) Case 2(ii): Blade 5 looseness, (d) Case 3(i): Blades 2 and 4 crack, (e) Case 3(ii): Blade 2 crack, (f) Case 3(iii): Blade 4 crack, (g) Case 3(iv): Blade 4 crack after 100 min of machine operation.
Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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and 3 are also shown in Fig. 15 for easy comparison with Case 1 healthy condition. Similarly, Fig. 16 compares the IAS response in the frequency band of 240–270 Hz for the faulty cases (Cases 2 and 3) with the healthy case (Case 1) at the EO10.
7. Observations and results It is observed from Fig. 15(a) that the amplification of the BR region seems to be in a banded form for Case 1 blade healthy condition. The mistuned effect in the blades natural frequencies is possibly resulted into a band response. A small amplification in the BR region at higher harmonics of 1 BR is also observed for the healthy case. A typical EO10 response in 2 BR region for the healthy case is shown in Fig. 16(a). The presence of higher harmonics of the BR for the healthy blades or higher harmonics of the shaft speed even for the healthy machine is often observed in the experimental rigs and rotating machines. It is often due to some misalignment in the rotor at coupling during the machine assembly [18]. However it is important to observe the dynamic behaviour and changes in case of the faulty blade conditions.
Fig. 16. Typical IAS responses at EO10: (a) Case 1: Healthy, (b) Case 2(i): Blade 1 looseness, (c) Case 2(ii): Blade 5 looseness, (d) Case 3(i): Blades 2 and 4 crack, (e) Case 3(ii): Blade 2 crack, (f) Case 3(iii): Blade 4 crack, (g) Case 3(iv): Blade 4 crack after 100 min of machine operation.
Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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Cases 2(i) and 2(ii) are the root looseness cases at Blades 1 and 5 respectively. The addition of 2 loosely held washers at the root has not affected the natural frequency of Blades 1 and 5 significantly but their EO5 and EO10 responses in Figs. 15 and 16 show significantly different behaviour compared to Case 1. It was observed that the 1 BR and 2 BR show 2 or more distinct peaks instead of a single banded peak for Case 1 healthy condition. These features are nearly common for both blade looseness cases—Blade 1 (Case 2(i)) and Blade 5 (Case 2(ii)) compared to Case 1 (healthy blades). Case 3 is the tests related to the crack in the blade where 4 tests were conducted as per Table 3. Case 3(i) was related with the crack in 2 blades, a crack in Blade 2 only for Case 3(ii), a crack in blade 4 only for Case 3(iii) and Case 3(iv) was the repeat test of Case 3(iii) after running the rig at 600 rpm for 100 min. Once again the distinct multiple peaks in the 1 BR and 2 BR regions related to the EO5 and EO10 responses respectively have been observed for all crack cases in the Case 3. It is evident from Figs. 15 and 16. The observations are close to the Case 2 for the blade root looseness. Case 3(iv) was basically the repetition of the Case 3(iii) after the period of 100 min rig operation. The identical observations in the Case 3(iii) and 3(iv) also confirm the repeatability of the dynamics behaviour of the rig. The crack breathing (opening and closing of crack) of the cracked blades and the interaction due to the root looseness in the blades seem to be responsible for the multiple peaks in the BR region and its higher harmonics. Further investigation is also done on a simple mathematical model to understand the banded peak and multiple peaks in the BR region for the healthy and faulty blade cases respectively.
8. Mathematical model A Jeffcott rotor of mass, mr and stiffness, kr is considered with 8 blades to understand the experimental behaviour in much simplified way. The model is shown in Fig. 17. The rotor is modelled as a single degree of freedom (SDOF) system connected with 8 SDOF systems representing the 8 blades. The values of the rotor parameters and the blade masses (½ mb1 mb2 . . . mb8 ) and corresponding stiffinesses (½ kb1 kb2 . . . kb8 ) are chosen such that the model gives the natural frequencies close to the experimental case. The natural frequency of the rotor is computed to be 97.22 Hz and 118.25–126.61 Hz for the blades which are nearly close to the experimental values. The damping assumed to be 0.1% and 0.5% for the rotor and blades respectively in the mathematical model. The unbalance responses for the rotor are then calculated during the machine run-up from 600 rpm (10 Hz) to 2400 rpm (40 Hz) for the following 2 cases. (i). Healthy but mistuned blade (118.25–126.6 Hz) condition. (ii). 10% crack in Blade 2: Breathing of the crack is also simulated while the response estimation by assuming the change in Blade 2 stiffness, kb2 ¼ kDk, when the displacement in the blade is positive (open crack) and kb2 ¼ k, kb2 ¼ kDk, when the displacement in the blade is zero or negative (closed crack), where k is the initial value of blade stuffiness and the change in the stiffness, Dk ¼ 0:10k for 10% crack.
The calculated run-up acceleration responses are then order tracked at EO5 which are shown in Fig. 18. The presence of peak at 97 Hz in Fig. 18 indicates the rotor critical speed. It is also evident from Fig. 18 that the healthy blade case gives a banded peak in the BR, however the 2 distinct peaks for the cracked blade case. Hence this simple analysis supports the experimental observations. Therefore, the presence of the distinct multiple peaks in the BR region and its higher harmonics can be considered as the useful feature to identify the blade fault(s).
Fig. 17. Simplified rotor model with 8 blades.
Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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Fig. 18. Typical estimated acceleration responses at EO5: (a) healthy blade and (b) crack in Blade 2.
9. Conclusion In this paper the measured shaft IAS signal during machine transient operation was used to understand the dynamics of the rotor blades with and without faults. Experiments were conducted for the 3 different blade conditions: (a) Case 1: Healthy with mistuned effects, (b) Case 2: Blade root looseness and (c) Case 3: Blade crack. The IAS signal when order tracked with the EO5 and its higher multiples shows the existence of the BR and its higher harmonics for all the 3 cases. It was observed that the one banded peak for healthy blades (Case 1) in the 1 BR changes to the two or more peaks in 1 BR and its higher harmonics for both faults conditions—the blade root looseness (Case 2) and the crack blade cases (Case 3). These features are nearly common for all faulty cases. A simple mathematical model and analysis also support the feature of a banded peak and the multiple peaks for the healthy and the cracked blade cases respectively. Hence the present observations are definitely encouraging and can be extended further for the BHM. The instrumentation cost and the signal processing are also not exorbitant and can be easily extended to any industrial applications. More experiments are also underway with multistage bladed discs to enhance confidence levels of the present observations. References [1] K. Sinha, W. Hahn, K. Elbhbah, G. Tasker, I. Ullah, Vibration investigation for low pressure turbine last stage blade failure in steam turbines of a power plant, GT2012-70129, in: Proceedings of the International Conference on Turbine Technical Conference and Exposition ASME TURBO EXPO, June 11–15, 2012, Copenhagen, Denmark. [2] B.O. Al-Bedoor, Blade vibration measurement in turbo-machinery: current status, Shock Vib. Dig. 34 (6) (2002) 455–461. [3] A.R. Rao, R.K. Sinha, Insitu measurement on turbo-generators for detection of blade vibrations, in: Proceedings of the VETOMAC-1, October 2000, Bangalore, India. [4] D. Knappett, J. Garcia, Blade tip timing and strain gauge correlation on compressor blades, Proc. Inst. Mech. Eng. Part G: J. Aerosp. Eng. 222 (2008) 497–506. [5] J.S. Rao, A. Pathak, A. Chawla, Blade life: a comparison by cumulative damage theories, Trans. ASME—J. Eng. Gas Turbine Power 123 (2001) 886–892. [6] G. Dimitriadis, I.B. Carrington, J.R. Wright, J.E. Cooper, Blade-tip timing measurement of synchronous vibrations of rotating bladed assemblies, Mech. Syst. Signal Process. 16 (4) (2002) 599–622. [7] P. Charles, J.K. Sinha, F. Gu, L. Lidstone, A.D. Ball, Detecting the crankshaft torsional vibration of diesel engines for combustion related diagnosis, J. Sound Vib. 321 (3–5) (2009) 1171–1185. [8] P. Charles, J.K. Sinha, F. Gu, A.D. Ball, Application of novel polar representation method for monitoring minor engine condition variations, Mech. Syst. Signal Process. 24 (3) (2010) 841–843. [9] L. Arebi, F. Gu, A. Ball, Rotor misalignment detection using a wireless sensor and a shaft encoder, in: Proceedings of the Computing and Engineering Annual Researchers’ Conference 2010: CEARC’10. University of Huddersfield, Huddersfield, 2010, pp. 6–13.
Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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[10] L. Arebi, Y. Fan, F. Gu, A. Ball, Investigation of wireless sensor deployed on a rotating shaft and its potential for machinery condition monitoring, in: 23rd International Congress on Condition Monitoring and Diagnostic Engineering Management, June 28–July 2, 2010, Japan. [11] K.P. Maynard, M.W. Trethewey, Blade and shaft crack detection using torsional vibration measurement part 1: feasibility studies, Noise Vib. Worldwide 31 (11) (2000) 9–15. [12] K.P. Maynard, M.W. Trethewey, Blade and shaft crack detection using torsional vibration measurement part 2: resampling to improve effective dynamic range, Noise Vib. Worldwide 32 (2) (2001) 23–26. [13] K.P. Maynard, M.W. Trethewey, Blade and shaft crack detection using torsional vibration measurement part 3: field application demonstrations, Noise Vib. Worldwide 32 (11) (2001) 16–23. [14] B.O. Al-Bedoor, Dynamic model of coupled shaft torsional and blade bending deformations in rotors, Comput. Methods Appl. Mech. Eng. 169 (1999) 177–190. [15] S. Huang, K. Ho, Coupled shaft-torsion and blade-bending vibrations of rotating shaft-disk-blade unit, ASME J. Eng. Gas Turbines Power 118 (1996) 100–106. [16] K. Sinha, et al., Vibration measurement on TG set of Narora Atomic Power Station (NAPS)-2, BARC report ref. RED/RIKM/1253/1994, BARC Mumbai, India, 1994. [17] D.J. Ewins, Modal Testing-Theory, Practice and Applications, 2nd edition, Research Studies Press Ltd, England, UK, 2000. [18] K. Sinha, K. Elbhbah, A future possibility of vibration based condition monitoring of rotating machines, Mech. Syst. Signal Process. 34 (1–2) (2013) 231–240.
Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp
Shaft instantaneous angular speed for blade vibration in rotating machine Ahmed A. Gubran, Jyoti K. Sinha n School of Mechanical, Aerospace and Civil Engineering (MACE), The University of Manchester, Sackville Street, Manchester M13 9PL, UK
a r t i c l e i n f o
abstract
Article history: Received 29 June 2012 Received in revised form 19 December 2012 Accepted 3 February 2013
Reliable blade health monitoring (BHM) in rotating machines like steam turbines and gas turbines, is a topic of research since decades to reduce machine down time, maintenance costs and to maintain the overall safety. Transverse blade vibration is often transmitted to the shaft as torsional vibration. The shaft instantaneous angular speed (IAS) is nothing but the representing the shaft torsional vibration. Hence the shaft IAS has been extracted from the measured encoder data during machine run-up to understand the blade vibration and to explore the possibility of reliable assessment of blade health. A number of experiments on an experimental rig with a bladed disk were conducted with healthy but mistuned blades and with different faults simulation in the blades. The measured shaft torsional vibration shows a distinct difference between the healthy and the faulty blade conditions. Hence, the observations are useful for the BHM in future. The paper presents the experimental setup, simulation of blade faults, experiments conducted, observations and results. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Instantaneous angular speed (IAS) Blade vibration Blade health monitoring (BHM) Blade faults Shaft torsional vibration Order tracking
1. Introduction Rotating blades are considered as the most common cause of failures in rotating machinery. The blade failure modes normally occur as a result of cracking, high cycle stresses, blade rubbing, blade root looseness, degradation from erosion and corrosion. Therefore, early fault detection is important in reducing blade related failures and hence there is a need of a reliable and simple blade health monitoring (BHM) technique. Sinha et al. [1] recently analyse the in-situ measured vibration data at the bearing pedestals during the steady state and the transient operations in the steam turbines to understand the machine dynamics, and to identify the root cause of the failure of the last stage blades in the low pressure turbines. Al-Bedoor [2] gave the review of different research methods that has been attempted for blade vibration measurements till year 2002. In-situ casing vibration near the last stage of a low pressure (LP) turbine in a steam turbogenerator (TG) set was observed to show the trace of blade resonance only during the fluctuation in the condenser pressure due to change in loads [3]. But such observation contains very limited information and may not be useful for diagnosis. Strain measurement on the blades during the machine operation is another option [4], this is where strain can be measured directly and hence the stress and possibly residual blade life can be estimated [5]. The blade tip time (BTT) has received attention in recent years and it can identify blades with high vibration [4,6]. However both the BTT and the strain measurement methods are intrusive and exorbitant methods. Hence there is a need for reliable and simple but robust method to meet the requirements of the BHM.
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Corresponding author. Tel.: þ44 161 3064639; fax: þ 44 161 3064601. E-mail addresses: [email protected], [email protected] (A.A. Gubran), [email protected] (J.K. Sinha).
0888-3270/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ymssp.2013.02.005
Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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A.A. Gubran, J.K. Sinha / Mechanical Systems and Signal Processing ] (]]]]) ]]]–]]]
The use of the encoder in rotating machines is seems to be a common practice to measure the shaft speed. The shaft instantaneous angular speed (IAS) signal from the encoder raw signal based on time-intervals change between successive pulses is nothing but the representing the shaft torsional vibration. This method is generally non-intrusive and nonexorbitant method and now the topic of research for different applications. A few of them include the identification of faulty combustion cylinder(s) in the diesel engines [7,8] using the crank shaft IAS signal and the IAS response of the shaft with fault(s) in rotating machine [9,10]. It has also been reported in the literature that transverse blade vibration is often reflected in the shaft torsional vibration. It was experimentally verified on small rigs, and the mistuning effect on the blade natural frequency was also observed [11,12]. Maynard and Trethewey [13] have also demonstrated the field application on the use of the torsional vibration for tracking crack in shaft and blades. Analytical simulations [14] and Huang and Ho [15] have also shown the potential of the shaft torsional vibration that could be used as the condition monitoring for turbine blades. However, Sinha et al. [16] could not identify the last stage blade resonance during normal operation of a steam turbine in a 220 MW Nuclear Power Plant in India. The transient operation of machine may be useful for such machines. Hence the shaft IAS has been extracted from the measured encoder data during the machine transient operation to understand the dynamics of the blades and to explore the possibility of reliable assessment of the blade health. A series of experiments were conducted on a test rig with an 8-bladed disc for three different conditions: (1) healthy with mistuned effects, (2) blade root looseness and (3) blade(s) with crack. These conditions are often observed in practice for the rotating machines like steam turbines, gas turbines, etc. and hence the early and reliable detection of the faulty conditions (2) and (3) is important. The extracted IAS signal from the encoder raw data during the machine run-up were then order tracked at the different engine order (EO) speeds so that the presence of the blade resonances, their higher harmonics and dynamics behaviour can be analysed. The measured shaft torsional vibration shows a distinct difference between the healthy and the faulty blade conditions and hence the observations may be useful for the BHM in future. The paper presents the IAS extraction process from the encoder measurement, rig details, blade faults simulations, experiments conducted and the observations on the blade dynamics which may possibly lead to the BHM in future.
2. Instantaneous angular speed (IAS) measurement An encoder that measures 360 pulses for every complete rotation of a shaft has been used for the present experiment. To aid the understanding of the IAS signal extraction from the measured encoder pulse train, a simplified measurement scheme of the encoder and the pulse train is shown in Fig. 1. The sensor simply measures the gap between each tooth on the gear during its rotation which results in the pulse train of the measured gap voltage with time as shown in Fig. 1. The extraction of instantaneous angular speed (IAS) signal using the pulse train in Fig. 1 is discussed in the following steps. (i) Each square pulse represents a tooth in the gear of the encoder, hence the difference of times, t 2 t 1 , t 3 t 2 , y.,t n þ 1 t n , etc. represents the time interval required to cross the 1st, 2nd, y., nth tooth respectively which is written as
Dtn ¼ tn1 tn
ð1Þ
Fig. 1. Pulse train created from shaft encoder.
Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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It is also assumed that the time interval for nth tooth is measured at the time, T n as Tn ¼
tn þ tn þ 1 2
ð2Þ
where n¼1, 2, 3, 4, 5,y, N number of teeth in the gear of the encoder. (ii) The angular displacement Dy for the each equally spaced tooth in the gear wheel of the encoder can be written as
Dy ¼ 3601=N ¼
2p N
ð3Þ
(iii) Hence the instantaneous angular speed (IAS) at time, T n in terms of revolution per second (RPS) can be calculated as Instantaneous angular speed ðIASÞ ðf sn Þ at ðT n Þ ¼
Dy ðDt n 2pÞ
ð4Þ
The extracted IAS signal from the measured pulse train from an encoder may look as shown in Fig. 2 if the shaft is rotating at a constant speed. It is expected to be the ideal case when there is no fluctuation in the speed during the shaft rotation and/or no shaft torisonal vibration i.e., Dt 1 ¼ Dt 2 ¼ Dt 3 ¼ ¼ Dt N . However in reality these time intervals, Dt n , may not be always constant due to the speed fluctuation and/or due to the presence of shaft torsional vibration and can be presented as Fig. 3. The time vectors, T n and corresponding IAS, f ns may not be at the equal time interval, hence the data are re-sampled with a uniform time interval before further signal processing. 3. Experimental setup In order to investigate the feasibility of torsional vibration measurement technology for incipient blade deterioration, an experimental test rig was built in the dynamics Lab at the school of MACE at the University of Manchester for this study. The test rig mainly consists of: (a) 1 hp 3-phase motor, (b) two SKF type YS 20 TF, ball bearings, (c) a steel shaft of diameter 20 mm, (d) a bladed disc with eight rectangular blades, and (e) a flexible coupling between the motor shaft and the rotating rig shaft. The schematic of rig with the instruments is shown in Fig. 4. A photograph of the test rig including the measurement system is also shown in Fig. 5. The dimensions and material properties for the shaft–disc–blade system are listed in Table 1. The photographs for a blade and a bladed disc are also shown in Fig. 6. 3.1. Instrumentations Figs. 4 and 5 also show the mounting of the encoder at the end of the rotor shaft and the accelerometers on the bearing housing. The measuring system composed of one rotary shaft encoder, Kubler-2400, which generate 360 pulses per revolution. A tacho sensor (Model S51-PA-2-A00-NK) retro-reflective optical sensor was used to monitor rotating speed.
Fig. 2. Idealised shaft IAS showing constant shaft speed without torsion.
Fig. 3. Typical shaft IAS showing the possibility of the shaft torsion.
Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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Fig. 4. Schematic of the test rig with instrumentations.
Fig. 5. Photograph of the test rig.
Table 1 Shaft–disk–blades data. Part
Property
Value
Shaft
Material Length Diameter
Stainless steel (E ¼210 GPa, r ¼ 7800 kg/m3) 600 mm 20 mm
Disc
Material Width Outer diameter, Do Inner diameter, Di
Steel (E ¼210 GPa, r ¼7800 kg/m3) 20 mm 50 mm 20 mm
Blade (8 numbers)
Material Length Width Thickness
Steel (E ¼210 GPa, r ¼7800 kg/m3) 110 mm 20 mm 2 mm
The output of the encoder and the tacho sensors are connected to the data acquisition board NI USB-6221 for data collection and storage into the PC. The photograph of the data acquisition board with PC is shown in Fig. 7.
4. Modal testing Modal testing has been conducted on the test rig for the eight blades in order to determine blade natural frequencies by using the Impulse-Response modal test [17]. Each blade was excited using an instrumented hammer (type PCB-0860C03) and the vibration responses were measured using a tiny accelerometer (Model 352C22, M/s PCB) weighing just 0.5 g. The blades natural frequencies were identified using the frequency response functions (FRF) calculated from the measured Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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Fig. 6. (a) A blade and (b) bladed disc.
Fig. 7. Rig measurement systems.
force and acceleration data. The experimentally identified first natural frequency for each blade is listed in Table 2. A small deviation in blade natural frequencies showing the presence of the blade mistuned effect due to possibly small deviation in blade manufacturing and/or fitting.
5. Faults simulation and experiments Three different blade faults were simulated for the experiments. These conditions of blade are: (a) Case 1: Healthy blades with mistuned effects, (b) Case 2: Blade root looseness and (c) Case 3: Crack on blade(s). These are summarised in Table 3 and also discussed in the following sections. Fig. 8 illustrates the faulty blade(s) position with respect to the tacho sensor location. Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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Table 2 Experimentally identified blades 1st natural frequency. Blade no.
Blade 1st natural frequencies (Hz)
1 2 3 4 5 6 7 8
123.75 126.25 125.00 127.50 128.75 123.75 125.00 125.00
Mean frequency (7 deviation)
125.625 (7 3.125)
Table 3 Blade faults conditions. Case
Description
Blade no.
1
Healthy with mistuned
–
2
Blade root looseness
(i) Blade no. 1 (ii) Blade no. 5
3
Crack on blade(s)
(i) Blade nos. 2 and 4 (two cracked blades together) (ii) Blade no. 2, 37 mm from blade root (iii) Blade no. 4, 22 mm from blade root (iv) Blade no. 4, 22 mm from blade root, after 100 min of machine operation
5.1. Healthy blade with mistuned effect The healthy blade with mistuned case (Case 1 as per Table 3) for the blades is tested initially where the variation in the 1st natural frequencies is listed in Table 2. It is the most likely condition of the healthy blades in any rotating machines like the steam turbines, gas turbines, etc.
5.2. Blade root looseness If the blades are not properly mounted and assembled on the shaft disc then the blades root may be loose that could result in rubbing during machine operation which may lead to the failure. Hence this root looseness fault is simulated by putting 2 free loose washers on the root of Blades 1 and 5 separately as per the Case 2(i) and Case 2(ii) in Table 3. Fig. 9 shows the root looseness simulation.
5.3. Blade crack simulation A small cut on blade of 0.6 mm width by a thin saw was made on 2 blades but at different locations. A very thin metal sheet placed on blade cut using adhesive glue from one side of cut so that breathing (opening and closing) of crack in the blade can be realized during vibration. The crack made on the 2 blades is shown in Fig. 10 and the cracked blades in the rig in Fig. 11. Here, a total of 4 tests were conducted for the cracked blade case as per Table 3 to understand the dynamic behaviour of crack blade(s) in different combinations; crack in a single blade but different location, crack in 2 blades simultaneously and the impact on the dynamic behaviour when a crack blade, Case 3(iv), is tested after 100 min of machine operation.
5.4. Experiments conducted The vibration experiments have been carried out for all cases listed in Table 3 (i.e., Healthy, Root looseness and Crack blade). Initially the experiments were conducted at different constant shaft speeds but the excitation of the shaft torisonal vibration was not observed to be significant, hence the further experiments were conduced during the machine run-up from 600 rpm (10 Hz) to 1800 rpm (30 Hz). The run-up rate was kept equal to 40 rpm/s. The measured analogue signals by the encoder and tacho sensors were then collected at 50,000 Samples/s and stored into the PC for the further signal processing. Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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7 (270°) 6 (225°)
8 (315°)
5 (180°)
1 (0°)
4 (135°)
2 (45°) 3 (90°)
Fig. 8. Schematic diagram of the blade positions with respect to the tacho sensor.
Fig. 9. Simulation of blade root looseness fault: (a) Blade 1 and (b) Blade 5.
Fig. 10. Blade crack simulations: (a) front side of a crack, (b) back side of a crack, (c) a very thin metal sheet in the crack, (d) crack locations 37 mm and 22 mm from blade root for Blades 2 and 4 respectively.
Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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Fig. 11. Different view of a typical cracked blade on the bladed disc in the rig.
Fig. 12. A typical rotor speed profile for the rig during run-up.
Fig. 13. A typical measured encoder signal.
6. Data analysis The measured tacho sensor and encoder data were analysed for all the cases to extract the shaft speed with time and the IAS signal with time as suggested in Section 2. A typical shaft speed from the tacho sensor and the raw signal from the encoder for the healthy blades condition (Case 1) are shown in Figs. 12 and 13 respectively. The extracted IAS signals are then processed with the different engine order (EO) speeds to understand the appearance of blade resonances, their higher harmonics and dynamics behaviour. It has been observed that the EO5 and its higher harmonics (EO10, EO15, y) contains the blade responses in the IAS signals. Fig. 14 shows a typical EO5 response for Case 1 healthy condition. The peak around 94 Hz and 108 Hz are related with the shaft torisonal resonance (with the flexible coupling to the motor) and the critical speed of the rig (the rig natural frequency). A hump around 120–130 Hz is related to the blade resonance (BR) region indicates that the blades are excited during the machine run-up and related in a banded resonance due to the blade mistuning. Fig. 15(a) shows the zoom view of Fig. 14 in the frequency range 120–135 Hz so that blade response in the resonance region can be clearly observed. The EO5 responses in the BR in the frequency band of 120–135 Hz for Cases 2 Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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Fig. 14. A typical IAS response at EO5 for Case 1: Healthy blade.
Fig. 15. Typical IAS responses at EO5: (a) Case 1: Healthy, (b) Case 2(i): Blade 1 looseness, (c) Case 2(ii): Blade 5 looseness, (d) Case 3(i): Blades 2 and 4 crack, (e) Case 3(ii): Blade 2 crack, (f) Case 3(iii): Blade 4 crack, (g) Case 3(iv): Blade 4 crack after 100 min of machine operation.
Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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and 3 are also shown in Fig. 15 for easy comparison with Case 1 healthy condition. Similarly, Fig. 16 compares the IAS response in the frequency band of 240–270 Hz for the faulty cases (Cases 2 and 3) with the healthy case (Case 1) at the EO10.
7. Observations and results It is observed from Fig. 15(a) that the amplification of the BR region seems to be in a banded form for Case 1 blade healthy condition. The mistuned effect in the blades natural frequencies is possibly resulted into a band response. A small amplification in the BR region at higher harmonics of 1 BR is also observed for the healthy case. A typical EO10 response in 2 BR region for the healthy case is shown in Fig. 16(a). The presence of higher harmonics of the BR for the healthy blades or higher harmonics of the shaft speed even for the healthy machine is often observed in the experimental rigs and rotating machines. It is often due to some misalignment in the rotor at coupling during the machine assembly [18]. However it is important to observe the dynamic behaviour and changes in case of the faulty blade conditions.
Fig. 16. Typical IAS responses at EO10: (a) Case 1: Healthy, (b) Case 2(i): Blade 1 looseness, (c) Case 2(ii): Blade 5 looseness, (d) Case 3(i): Blades 2 and 4 crack, (e) Case 3(ii): Blade 2 crack, (f) Case 3(iii): Blade 4 crack, (g) Case 3(iv): Blade 4 crack after 100 min of machine operation.
Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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Cases 2(i) and 2(ii) are the root looseness cases at Blades 1 and 5 respectively. The addition of 2 loosely held washers at the root has not affected the natural frequency of Blades 1 and 5 significantly but their EO5 and EO10 responses in Figs. 15 and 16 show significantly different behaviour compared to Case 1. It was observed that the 1 BR and 2 BR show 2 or more distinct peaks instead of a single banded peak for Case 1 healthy condition. These features are nearly common for both blade looseness cases—Blade 1 (Case 2(i)) and Blade 5 (Case 2(ii)) compared to Case 1 (healthy blades). Case 3 is the tests related to the crack in the blade where 4 tests were conducted as per Table 3. Case 3(i) was related with the crack in 2 blades, a crack in Blade 2 only for Case 3(ii), a crack in blade 4 only for Case 3(iii) and Case 3(iv) was the repeat test of Case 3(iii) after running the rig at 600 rpm for 100 min. Once again the distinct multiple peaks in the 1 BR and 2 BR regions related to the EO5 and EO10 responses respectively have been observed for all crack cases in the Case 3. It is evident from Figs. 15 and 16. The observations are close to the Case 2 for the blade root looseness. Case 3(iv) was basically the repetition of the Case 3(iii) after the period of 100 min rig operation. The identical observations in the Case 3(iii) and 3(iv) also confirm the repeatability of the dynamics behaviour of the rig. The crack breathing (opening and closing of crack) of the cracked blades and the interaction due to the root looseness in the blades seem to be responsible for the multiple peaks in the BR region and its higher harmonics. Further investigation is also done on a simple mathematical model to understand the banded peak and multiple peaks in the BR region for the healthy and faulty blade cases respectively.
8. Mathematical model A Jeffcott rotor of mass, mr and stiffness, kr is considered with 8 blades to understand the experimental behaviour in much simplified way. The model is shown in Fig. 17. The rotor is modelled as a single degree of freedom (SDOF) system connected with 8 SDOF systems representing the 8 blades. The values of the rotor parameters and the blade masses (½ mb1 mb2 . . . mb8 ) and corresponding stiffinesses (½ kb1 kb2 . . . kb8 ) are chosen such that the model gives the natural frequencies close to the experimental case. The natural frequency of the rotor is computed to be 97.22 Hz and 118.25–126.61 Hz for the blades which are nearly close to the experimental values. The damping assumed to be 0.1% and 0.5% for the rotor and blades respectively in the mathematical model. The unbalance responses for the rotor are then calculated during the machine run-up from 600 rpm (10 Hz) to 2400 rpm (40 Hz) for the following 2 cases. (i). Healthy but mistuned blade (118.25–126.6 Hz) condition. (ii). 10% crack in Blade 2: Breathing of the crack is also simulated while the response estimation by assuming the change in Blade 2 stiffness, kb2 ¼ kDk, when the displacement in the blade is positive (open crack) and kb2 ¼ k, kb2 ¼ kDk, when the displacement in the blade is zero or negative (closed crack), where k is the initial value of blade stuffiness and the change in the stiffness, Dk ¼ 0:10k for 10% crack.
The calculated run-up acceleration responses are then order tracked at EO5 which are shown in Fig. 18. The presence of peak at 97 Hz in Fig. 18 indicates the rotor critical speed. It is also evident from Fig. 18 that the healthy blade case gives a banded peak in the BR, however the 2 distinct peaks for the cracked blade case. Hence this simple analysis supports the experimental observations. Therefore, the presence of the distinct multiple peaks in the BR region and its higher harmonics can be considered as the useful feature to identify the blade fault(s).
Fig. 17. Simplified rotor model with 8 blades.
Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i
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Fig. 18. Typical estimated acceleration responses at EO5: (a) healthy blade and (b) crack in Blade 2.
9. Conclusion In this paper the measured shaft IAS signal during machine transient operation was used to understand the dynamics of the rotor blades with and without faults. Experiments were conducted for the 3 different blade conditions: (a) Case 1: Healthy with mistuned effects, (b) Case 2: Blade root looseness and (c) Case 3: Blade crack. The IAS signal when order tracked with the EO5 and its higher multiples shows the existence of the BR and its higher harmonics for all the 3 cases. It was observed that the one banded peak for healthy blades (Case 1) in the 1 BR changes to the two or more peaks in 1 BR and its higher harmonics for both faults conditions—the blade root looseness (Case 2) and the crack blade cases (Case 3). These features are nearly common for all faulty cases. A simple mathematical model and analysis also support the feature of a banded peak and the multiple peaks for the healthy and the cracked blade cases respectively. Hence the present observations are definitely encouraging and can be extended further for the BHM. The instrumentation cost and the signal processing are also not exorbitant and can be easily extended to any industrial applications. More experiments are also underway with multistage bladed discs to enhance confidence levels of the present observations. References [1] K. Sinha, W. Hahn, K. Elbhbah, G. Tasker, I. Ullah, Vibration investigation for low pressure turbine last stage blade failure in steam turbines of a power plant, GT2012-70129, in: Proceedings of the International Conference on Turbine Technical Conference and Exposition ASME TURBO EXPO, June 11–15, 2012, Copenhagen, Denmark. [2] B.O. Al-Bedoor, Blade vibration measurement in turbo-machinery: current status, Shock Vib. Dig. 34 (6) (2002) 455–461. [3] A.R. Rao, R.K. Sinha, Insitu measurement on turbo-generators for detection of blade vibrations, in: Proceedings of the VETOMAC-1, October 2000, Bangalore, India. [4] D. Knappett, J. Garcia, Blade tip timing and strain gauge correlation on compressor blades, Proc. Inst. Mech. Eng. Part G: J. Aerosp. Eng. 222 (2008) 497–506. [5] J.S. Rao, A. Pathak, A. Chawla, Blade life: a comparison by cumulative damage theories, Trans. ASME—J. Eng. Gas Turbine Power 123 (2001) 886–892. [6] G. Dimitriadis, I.B. Carrington, J.R. Wright, J.E. Cooper, Blade-tip timing measurement of synchronous vibrations of rotating bladed assemblies, Mech. Syst. Signal Process. 16 (4) (2002) 599–622. [7] P. Charles, J.K. Sinha, F. Gu, L. Lidstone, A.D. Ball, Detecting the crankshaft torsional vibration of diesel engines for combustion related diagnosis, J. Sound Vib. 321 (3–5) (2009) 1171–1185. [8] P. Charles, J.K. Sinha, F. Gu, A.D. Ball, Application of novel polar representation method for monitoring minor engine condition variations, Mech. Syst. Signal Process. 24 (3) (2010) 841–843. [9] L. Arebi, F. Gu, A. Ball, Rotor misalignment detection using a wireless sensor and a shaft encoder, in: Proceedings of the Computing and Engineering Annual Researchers’ Conference 2010: CEARC’10. University of Huddersfield, Huddersfield, 2010, pp. 6–13.
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[10] L. Arebi, Y. Fan, F. Gu, A. Ball, Investigation of wireless sensor deployed on a rotating shaft and its potential for machinery condition monitoring, in: 23rd International Congress on Condition Monitoring and Diagnostic Engineering Management, June 28–July 2, 2010, Japan. [11] K.P. Maynard, M.W. Trethewey, Blade and shaft crack detection using torsional vibration measurement part 1: feasibility studies, Noise Vib. Worldwide 31 (11) (2000) 9–15. [12] K.P. Maynard, M.W. Trethewey, Blade and shaft crack detection using torsional vibration measurement part 2: resampling to improve effective dynamic range, Noise Vib. Worldwide 32 (2) (2001) 23–26. [13] K.P. Maynard, M.W. Trethewey, Blade and shaft crack detection using torsional vibration measurement part 3: field application demonstrations, Noise Vib. Worldwide 32 (11) (2001) 16–23. [14] B.O. Al-Bedoor, Dynamic model of coupled shaft torsional and blade bending deformations in rotors, Comput. Methods Appl. Mech. Eng. 169 (1999) 177–190. [15] S. Huang, K. Ho, Coupled shaft-torsion and blade-bending vibrations of rotating shaft-disk-blade unit, ASME J. Eng. Gas Turbines Power 118 (1996) 100–106. [16] K. Sinha, et al., Vibration measurement on TG set of Narora Atomic Power Station (NAPS)-2, BARC report ref. RED/RIKM/1253/1994, BARC Mumbai, India, 1994. [17] D.J. Ewins, Modal Testing-Theory, Practice and Applications, 2nd edition, Research Studies Press Ltd, England, UK, 2000. [18] K. Sinha, K. Elbhbah, A future possibility of vibration based condition monitoring of rotating machines, Mech. Syst. Signal Process. 34 (1–2) (2013) 231–240.
Please cite this article as: A.A. Gubran, J.K. SinhaShaft instantaneous angular speed for blade vibration in rotating machine, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.02.005i