Considering the importance of vibration monitoring in the rotating machinery fault ... the two bearing and driven by 50 Watt, 230 Volt AC/DC electric motor ...
Sunil Pandey et al. / International Journal of Engineering Science and Technology (IJEST)
Vibration Monitoring of a Rotor System using RMS Accelerations (m/s2) Sunil Pandey1 Department of Mechanical and Automobile Engineering ITM University Sec-23A HUDA Gurgaon-122017 Haryana India Prof. B. C. Nakra2 Department of Mechanical and Automobile Engineering ITM University Sec-23A HUDA Gurgaon-122017 Haryana India Abstract:Vibration monitoring is a useful technique for application to rotating machines and provides valuable information regarding symptoms of machinery failures which in practice may avoid costly breakdowns. This paper involves design and fabrication of a rotor rig and investigations of vibrations at the bearings of the rig due to the effect of simulated faults, the test rig is designed in case of dynamic loading and also includes the various component used and fabrication of rotor rig The line diagram and actual photo graphs of Rotor Test Rig are also include in this paper. The faults like parallel misalignments, angular misalignment, combined parallel and angular misalignments and unbalances have been simulated. To study the effects of simulated faults, RMS (Root mean square) vibration accelerations in vertical, horizontal and axial direction of the rolling element bearings have been monitored using a piezoelectric accelerometer. Keyword: Test rig, accelerometer, pico-scope, charge amplifier, Vibration meter, and RMS acceleration (vertical, Horizontal and Axial). 1-Introduction:Increased complexities of rotating machinery and demands for higher speeds and greater power have created complex vibration problems. Engineering judgments based on understanding of physical phenomena are needed to provide the diagnosis and methods for correcting the rotating machinery faults. There is a growing tendency today to extract information about the prognostic parameters based on system analysis through various diagnostic techniques, so as to assess the health of the plant or equipment. Vibration monitoring helps in reducing the machine down time. The objective of vibration monitoring is to provide valuable information for the diagnosis of symptoms that helps in maintenance planning. A vibration signature measured at the external surface of machine or at any other suitable place contains a good amount of information to reveal the running condition of the machine. Thus, it provides very useful information regarding symptom of machinery failure preventing costly breakdowns. Considering the importance of vibration monitoring in the rotating machinery fault diagnostics, it has been applied in this paper for studying the effects of machinery faults on the rotor vibrations. There is a need for comprehensive experimental study in the rotating machinery faults. In this paper, effects of parameters like misalignments, and unbalances have been studied. Comprehensive experimentation is carried out monitoring and analysis of vibrations for a rotor supported by ball bearings. The RMS acceleration have been carried out for the vibration signatures due to different faults like parallel misalignment, angular misalignment, and combined parallel and angular misalignment and unbalance in supports( bearings). 2- Research Objectives:The objective of this research papers to construct a small rotor test rig supported in conventional ball bearings that could be used to simulate and determine machinery faults. Specifically parallel misalignments, angular misalignments, combined parallel and angular misalignments and unbalance are the targeted faults under investigation both supports. RMS acceleration has been carried out for the vibration signatures due to different faults mentioned above.
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3-Literature Review:The literature review has been carried-out in the areas of vibration monitoring of rotating machinery. Techniques of faults diagnosis and analysis of resulting vibration signatures have been reviewed. Vibration monitoring aims to define the current condition of machine and compare it with previously measured condition. Some element of prediction is inferred by noting trends in the observed parameter. Vibration signal analysis has become an established method for monitoring the condition of rotating machines. Traditionally, the vibration monitoring of rotating machinery is heavily dependent on the spectral analysis or the Fourier transform of the vibration signals. Beatty [1] has studied the interaction of rotor with its housing, which can have a significant effect on the rotor dynamics. The experimentation has been carried out on Bently-Nevada rotor kit with bearing clearance as small as possible. Pressing a brass screw against the rotor created rubbing fault. Emmanouilidis et al. [2] have proposed that among reliable diagnostic methodologies for automatic fault diagnosis. Including statistical, polynomial, neural network, fuzzy and neurofuzzy techniques offer a framework for analysis. It is proposed that there must be a trade off between model interpretability and performance while developing neurofuzzy system for computing in which first one is focused on building function fuzzy models while the second aims to build fully transparent fuzzy system. The described model is useful for the diagnosis of faults in noisy and multiple fault scenarios. The proposed model is still under development. Vyas and Satish Kumar[3] has carried out experimental studies to generate data and discussed the development of neural network simulator for prediction of faults like mass unbalance, bearing cap loose, play in spider coupling and rotor with both mass unbalance and misalignment and health machine network . The test data were generated on a laboratory rotor rig which consist of a 10mm diameter shaft carrying a centrally located steel disk (0.5 kg mass) and supported in identical rolling element bearing (6200 SKF ball bearing) at the two bearing and driven by 50 Watt, 230 Volt AC/DC electric motor through a flexible spider coupling. Fault simulated were: Mass unbalance, Loose Bearing cap & Misalignment & both mass unbalance and misalignment Srinivasan [4] has done comprehensive experimental studies in the rotating machinery for the faults like misalignment (parallel misalignment from 0.025mm to 0.65mm, angular misalignment from 0.02 degree to 0.6 degree), unbalance (105.06 gm-cm to 491.98 gm-cm), mechanical looseness, rotor rub, bearing clearance (from 0.02 to 0.08mm) and crack (transverse cracks of width 0.75mm and depth ranging from 1.02 to 4.02 mm at the mid span of the shaft). Combination of faults like combined parallel and angular misalignment, combination of faults like crack and unbalance in rotors has also been carried. All the experiments have been carried on two rotor rigs and RMS (root mean square) velocities in three different directions horizontal, vertical and axial has been gathered. Adewusi [5] has explained the application of neural networks for rotor crack detection. The basic working principals of neural networks are presented. Experimental vibration signal of rotor with and without propagation crack were used to train the multi-layer feed-forward algorithm. The trained neural networks were tested with other set of vibration data, A simple two layer feed-forward neural network with two neurons in the input layer and one neuron in the output layer trained with the signals of cracked rotor and a normal rotor and a normal rotor without a crack. Trained three-layer network were able to detect both the propagation and non-propagation cracks. The FFT of the vibration signal showing variation in amplitude of the harmonics as time progresses are also presented for comparison. Kalkat.M [6] has designed a direct-coupled rotor system to analyze the dynamic behaviour of rotating system with respect to vibration parameter. The vibration parameters are amplitude, velocity, and acceleration in the vertical direction. The system consisted of a machine analyzer, shaft, disk, master-trend software, and power unit. Four different points were detected and measured by the experimental setup. The vibration parameters were found and saved from master-trend software. These parameters were found and employed as the desired parameter of the network. A neural network is designed for analyzing a system’s vibration parameter. The results showed that the network could be used as an analyzer of such system in experimental application. Kashyap [7] has done experimental studies in the rotating machinery for the fault like parallel misalignment, angular misalignment, combined parallel and angular misalignment, mass unbalance, crack, crack and unbalance have been diagnosed. Feed forward back propagation network (FFBPN), Levenberg-Marquardt algorithm has been used. Three layer networks is used with logsig, tansig, and purelin transfer function in input, hidden and output layer respectively. Same vibration data has been used with the radial basis function network (RBNF) also for the fault diagnosis. Halim Enayet [8] the objective of this report is to explain the experimental setup configured to generate data for different simulated fault of a rotating machine, using the experimental Rotor Kit model 24750 designed by Bently Nevada. The simulated faults are unbalance of the rotor, shaft bow (overhung configuration of the rotor), and oil whirl of the bearing and rub on the rotor by the stator. Radial shaft vibration is measured using proximity
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transducers and Siglab vibration analyzer, designed by DSP Inc. at different rotating speed. Vibration from the shaft would change with a change in configuration (including change of position of load) and rotor speed. Sanjin barut [9] has explained the preliminary model testing of new rotor dynamic test rig for rotor-stator rub investigation. The main goals of this testing are determination of the base plate rigid body natural frequencies and choosing appropriate elastic element in order to set this rigid body frequencies as low as possible. Therefore, two sets of rubber elastic element are analyzed; further, natural frequencies of the rotor, stator and coupled rotor-stator (without rotation) are also investigated. Those natural frequencies are analyzed especially in horizontal and vertical direction with respect to possible lateral movement of the rotor. Travis Joel Bash [10] has introduced a method of modal analysis testing for a shaft supported in conventional bearings by using an Active Magnetic Bearing (AMB) as an actuator. The goal of this research was to prove that rotor health monitoring could be achieved while the shaft was rotating with the addition of the AMB. Many different types of faults exist for rotating machinery, but the two chosen for this work were shaft rub and shaft crack. The test rig consisted of a shaft that is 24 inches (610mm) long and 0.625 inches (15.9mm) in diameter supported with ball bearings. An AMB was placed at approximately midspan with two position probes located nearby for AMB control. 4-Line diagram of Experimental setup:The line diagram of experimental test rig is shown in fig 1. The test rig consists of a shaft with central rotor disc, which is supported on two ball bearings. A dc motor coupled by a flexible coupling drives the shaft. The parameters used in studies are given in table 1
Fig 1 Line Diagram of Rotor Rig Table 1-Parameters used in experimental and numerical analysis
Shaft Diameter, d Length L Material Density of material Young modulus Disc Diameter Thickness Material Density
10mm 330 mm Mild steel 7860Kg/m3 2.1*1011 N/m2 70 mm 15 mm Mild steel 7860Kg/m3
According to ASME code, the bending and torsional moments are to be multiplied by factor Kb and Kt respectively, to account for shock and fatigue in operating condition. The equation is written as [11]:
τd=
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16 d 3
k M b
2
k t T
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Where kb = combined shock and fatigue factor applied to bending moment; and kt = combined shock and fatigue factor applied to torsional moment τd = maximum shear stress of material d = diameter of the shaft M= maximum bending moment T = twisting moment Table 2. The value of kb and kt for rotating shaft are as follow:
kb
kt
(i) load gradually applied
1.5
1.0
(ii)load suddenly applied (sudden shock)
1.5-2.0
1.0-1.5
(iii)load suddenly applied (heavy shock)
2.0-3.0
1.5-3.0
5-Natural frequency (ωn) and critical speed [12]:-
ωn =
k m
Where k =stiffness of the shaft in the lateral direction
48 EI l3
k
=
M
= mass of the rotor with shaft
E
= young’s modulus of the mild steel = (2.1*1011 N/m2)
I
= Moment of inertia of the shaft
d
=0.01m
L
= 0.33m
Critical speed of shaft = 81.91 rps Critical speed of shaft =4915 rpm 6-Experimental Set-up:The actual rotor rig is also shown in fig 2 this rig consist of a shaft of 10 mm diameter and 330 mm length mounted in between the two SKF single row groove ball bearing. A disc of 70 mm diameter and 15 mm thick is fixed at the mid span of the shaft. The disc consists of 16 drilled holes on the periphery at a radius of 25 mm to fix the balancing mass. The rotor rig is driven by 0.25 HP motor running at a speed of 3000 RPM. A jaw type coupling connects the driver and driven shaft. The critical speed of rotor rig has been found to be 4915 RPM.
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Fig 2 Actual photograph of Rotor Test Rig
7-Instruments Used:The measuring instruments used in the experimental set-up are shown in fig 3. An accelerometer is mounted with a stud on the ball bearing housing. The output of the accelerometer is connected to the charge amplifier. The charge amplifier output is connected to a data acquisition system to acquire the signal and to carry out the frequency analysis using FFT (Fast Fourier Transform) software. The purpose of charge amplifier is to present high impedance to the piezo-electric transducer to avoid impedance loading and to eliminate the influence of cable capacitance and another output is connected to vibration meter for measuring RMS acceleration (m/s2).
Fig 3 Instrumentation for Rotor Rig
In this chapter the various types of instruments which are practically used in the set-up for determining the experimental values arte explained below. (i) Pico-scope (iii) Charge Amplifier
(ii) Accelerometer (iv) Vibration Meter
8-Simulation of Faults on rotor at the Supports (Bearings):8.1- Parallel Misalignments:The experimental setup has been shown in Figure 1. The instrumentation for the experiment has been shown in Figure3.The parallel misalignments have been created by moving both bearing 1 and 2 simultaneously. Misalignments ranging from 0.25 mm to 0.75 mm were created. The rotor was run at 1500 RPM. In parallel misalignments the overall RMS accelerations have used for classifying the faults which is recorded with vibration meter.
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Table-3 (a) Values of overall RMS Accelerations (m/s2) in vertical, horizontal and axial directions of different values of parallel misalignments of rotor speed at 1500 RPM of bearing 1. Misalignments Vertical Horizontal Axial (mm) RMS RMS RMS Accelerations Accelerations Accelerations (m/s2) (m/s2) (m/s2) 0 3.6 4.2 4.4 0.25
4.0
4.9
6.4
0.45
4.6
6.1
7.3
0.50
5.9
7.2
8.2
0.75
6.6
9.1
9.8
RMS Accelerations (m/sec2)
RMS Acceleration of Different Parallel Misalignment (Bearing 1) 10 8 Vertical Horizontal Axial
6 4 2 0 0
0.2
0.4
0.6
0.8
Parallel Misalignments (mm)
Fig-4- The graph of overall RMS Accelerations of Different Parallel Misalignments at 1500 RPM of Bearing1
Table-3(b)-Values of overall RMS Accelerations (m/s2) in vertical, horizontal and axial directions of different values of parallel misalignments of rotor speed at 1500 RPM of Bearing 2. . Misalignments (mm)
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Vertical
Horizontal
Axial
0
RMS Accelerations (m/s2) 6.3
RMS Accelerations (m/s2) 5.3
RMS Accelerations (m/s2) 5.2
0.25
7.2
6.4
6.3
0.45
8.4
7.1
7.5
0.5
9.2
8.3
8.5
0.75
10.9
9.1
9.2
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RMS Acceleration (m/sec2)
RMS Acceleration of Different Parallel Misalignment (Bearing 2) 12 10 8
Vertical Horizontal Axial
6 4 2 0 0
0.2
0.4
0.6
0.8
Parallel Misalignment (mm)
Fig 5- The graph of overall RMS Acceleration of Different Parallel Misalignments at 1500 RPM of Bearing 2
8.2-Angular Misalignment:The angular misalignments are created moving the bearing 2 and keeping the bearing 1 fixed. The angular misalignments are measured with the following formula and with the help of figure 6. This gives angular misalignment in degrees.
Fig -6 Measurement of Angular Misalignment
θ = tan
Where
bf L
bf =Distance move by bearing 2 L=Length of the shaft θ=Angular misalignment in degree
The different values of angular misalignment ranging from 2 degree to 5.36 degrees were created. The rotor was run at 1500 RPM. In angular misalignment the overall RMS accelerations have used for classifying the faults which is recorded with vibration meter, the experimental values of overall RMS accelerations are shown in table 4 (a) and 4 (b)
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Table-4(a)-Values of overall RMS Accelerations (m/s2) in vertical, horizontal and axial directions of different values of angular misalignments of rotor speed at 1500 RPM of Bearing 1. Misalignments Degree
Vertical
Horizontal
Axial
RMS Accelerations (m/s2)
RMS Accelerations (m/s2)
0
3.4
4.2
RMS Accelerations (m/s2) 4.6
2
4.2
5.3
6.5
2.38
4.6
6.5
7.5
4.39
6.2
7.3
8.3
5.34
8.2
8.2
9.2
RMS
Accelerations
RMS Acceleration of Different Angular Misalignment (Bearing 1) 12 8 4 0
Vertical Horizontal Axial 0
2
4
6
Angular Misalignments (Degree) Fig 7- The graph of overall RMS Acceleration of Different Parallel Misalignments at 1500 RPM of Bearing 1
Table-4(b)-Values of overall RMS Acceleration amplitudes (m/s2) in vertical, horizontal and axial directions of different values of angular misalignments of rotor speed at 1500 RPM of Bearing 2. Misalignments Degree
Vertical
Horizontal
Axial
RMS Accelerations (m/s2)
RMS Accelerations (m/s2)
RMS Accelerations (m/s2)
0
4.1
5.3
5.6
2
4.3
5.6
6.4
2.38
4.5
5.8
6.8
4.39
5.3
6.5
7.2
5.34
6.4
7.5
8.3
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RMS A c e le ra tio n s
RMS Acceleration of Different Angular Misalignment (Bearing 2) 12 8 4 0 0
2
4
6
Vertical Horizontal Axial
Angular Misalignments (Degree) Fig 8- The graph of overall RMS Accelerations of Different Angular Misalignments at 1500 RPM of Bearing 2
8.3-Combined Parallel and Angular Misalignments:Combined parallel and angular misalignments are the special cases of combination of faults. In most of the machinery misalignment cases, this type of fault exists. Initiaty, moving both the bearing block simultaneously created parallel and angular misalignments. In this case, both parallel and angular misalignments were created from 0.45mm to 0.75 mm and 1.33 degree, to 5.02 degree respectively. The rotor was run at 1500 RPM. The RMS accelerations for different values of combined parallel and angular misalignments have been also putted of the respective tables of bearing 1 and Bearing 2.
Table-5(a)-Values of overall RMS Accelerations (m/s2) in vertical, horizontal and axial directions of different values of combined parallel and angular misalignments of rotor speed at 1500 RPM of Bearing 1. Misalignments Degree
Vertical
Horizontal
Axial
Parallel & Angular
RMS Accelerations (m/s2)
RMS Accelerations (m/s2)
RMS Accelerations (m/s2)
5.5
4.5
6.1
5.9
5.3
6.8
6.4 7.6 8.2
5.9 7.6 8.6
7.6 9.2 10.2
0&0 0.45 & 1.33 0.50 & 2.37 0.65 & 3.7 0.75 & 5.02
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Fig 9- The graph of overall RMS Acceleration of Different combined parallel and Angular Misalignments at 1500 RPM of Bearing 1
Table-5(b)-Values of overall RMS Accelerations (m/s2) in vertical, horizontal and axial directions of different values of parallel and angular misalignments of rotor speed at 1500 RPM Bearing 2. Misalignments mm & Degree
Vertical
Horizontal
Axial
RMS Accelerations (m/s2) 4.2 5.3 6.5 7.5 8.6
RMS Accelerations (m/s2) 5.2 5.5 6.1 8.5 9.6
RMS Accelerations (m/s2) 5.2 6.9 8.2 9.2 9.8
0&0 0.45 & 1.33 0.50 & 2.37 0.65 & 3.7 0.75 & 5.02
RMS Acceleration
RMS Acceleration of Different Combined Parallel & Angular Misalignment (Bearing 2) 12 10 8 6 4 2 0
Vertical Horizontal Axial
0
2
4
6
Angular Misalignment Fig 10- The graph of overall RMS Acceleration of Different combined parallel and combined parallel and Angular Misalignments at 1500 RPM of Bearing 2
8.4- Unbalance:Before simulating unbalance in the rotor, the rotor was balanced by four run methods. The residual unbalance has been found to be 19.59 gm-cm at angle 135 degrees from the reference. The experiments were repeated for
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different unbalance masses. The rotor was run at 1500 RPM. The RMS accelerations have been carried out for the vibration signature of different unbalances. The unbalances were simulated in the rotor by fixing different unbalance masses at a radius of 25 mm on the periphery of the rotor. The frequency components in horizontal, vertical and axial directions are as shown in Table 6(a) and Table 6(b) for bearing 1 and bearing 2 respectively. 8.4.1-Balancing of Thin Rotor [13]:It may be some time difficult to either couple a sine-wave generator or use a phase meter. Under such circumstances, the balancing mass required for a single-plane rotor can be determined by measuring only the vibration amplitudes. However, to do this, two additional runs, using the same trail mass, are required as shall now explain. Referring to Fig 11(a) let the following four readings be taken for the vibration amplitudes (with the same speed of rotation): Amplitude
Test Condition
A1
Without any trial mass
A2
mt at P (=00)
A3
mt at Q (=1800)
A4
mt at R (=900)
Fig -11(a) Trail masses
Fig -11(b) Balancing of thin disc
For the last three run, the radial distance of the trail mass is kept unchanged as indicated in the figure Draw a triangle abc with sides ab (=2A1). ac (=A2), and bc (=A3) as shown in Fig11(b). Let d be the midpoint of ab. In this figure, dc represents the effect of only the trial mass at P. Hence, the magnitude of the required balancing mass to be placed at the same radius as that of the trail mass is obtained as
ad dc
mb=mt
The balancing mass should be located at an angle Φ - abc . This angle should be measured in the counterclockwise or clockwise direction depending on whether the magnitude of A4 is given by ae or af. The points e and f are obtained by rotating dc about the point d through 90o in the counter- clockwise and clockwise direction, respectively
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Table-6(a)-Values of overall RMS Accelerations (m/s2) in vertical, horizontal and axial directions of different values of unbalances of rotor speed at 1500 RPM Bearing 1. Unbalances (gm-cm)
Vertical
Horizontal
Axial
RMS Accelerations (m/s2)
RMS Accelerations (m/s2)
RMS Accelerations (m/s2)
19.59
5.6
3.2
4.2
21.58
6.3
4.5
5.1
23.93
7.2
5.8
6.0
29.13
8.6
8
9.2
34.85
9.4
8.5
9.9
RMS Accelerations (m/sec2)
RMS Acceleration of Different Unbalanc (Bearing 1) 10 8 6
Vertical Horizontal Axial
4 2 0 0
10
20
30
40
Unbalances (gm-cm) Fig -12- The graph of overall RMS Accelerations of Different unbalances at 1500 RPM of Bearing 1
Table-6(b)-Values of overall RMS Accelerations (m/s2) in vertical, horizontal and axial directions of different values of unbalances of rotor speed at 1500 RPM. Bearing 2. Unbalances (gm-cm)
Vertical
Horizontal
Axial
19.59
RMS Acceleration (m/s2) 5.5
RMS Acceleration (m/s2) 4.5
RMS Acceleration (m/s2) 6.4
21.58
5.6
5.2
7.5
23.93
6.2
6.2
8.5
29.13
7.4
6.5
9.4
34.85
8.6
7.4
10
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RM S Accelerations (m /sec2)
RMS Acceleration of Different Unbalance (Bearing 2) 12 10 8 6 4 2 0
Vertical Horizontal Axial 0
10
20
30
40
Unbalances (gm-cm) Fig-13- The graph of overall RMS Accelerations of Different unbalances at 1500 RPM of Bearing 2.
9-Discussion of Experimental results:The test rig has been fabricated for simulation of faults. The faults simulated on rig included parallel misalignments, angular misalignments, combined parallel and angular misalignments and unbalances on supports. The overall RMS accelerations at the bearing 1 and bearing 2 have been measured in vertical, horizontal and axial directions and increase when misalignments increased as shown in all the graphs given above. Parallel Misalignments In case of parallel misalignments the amplitudes are higher at bearing 2 (away from the motor) and lesser at bearing 1 (near to the motor) in all the directions (horizontal, vertical and Axial Directions). The highest value of overall RMS accelerations is produced in bearing 2. It can also see that the amplitudes are higher in axial direction in both the bearings and increase when misalignments increased. Angular Misalignments In case of Angular misalignments the amplitudes are higher at bearing 2 (away from the motor) and lesser at bearing 1 (near to the motor) in all the directions (horizontal, vertical and Axial Directions). The highest value of overall RMS accelerations is also produced in bearing 2. It can also see that the amplitudes are higher in axial direction in both the bearings and increase when misalignments increased. Combined Parallel and Angular Misalignments In case of combined parallel and Angular misalignments the amplitudes are also higher at bearing 2 (away from the motor) and lesser at bearing 1 (near to the motor) in all the directions (horizontal, vertical and Axial Directions). The highest value of overall RMS accelerations is also produced in bearing 2. It can also see that the amplitudes are higher in axial direction in both the bearings and increase when
misalignments increased. Unbalances In case of unbalance the amplitudes are higher at bearing 2 (away from the motor) and lesser at bearing 1 (near to the motor) in all the directions (horizontal, vertical and Axial Directions). The highest value of overall RMS accelerations is also produced in bearing 2. It can also see that the amplitudes are higher in axial direction in both the bearings and increase when misalignments increased. 10-Conclusion:In this research paper, the results of various fault analysis such as parallel misalignments, angular misalignment, combined parallel and angular misalignments and unbalances and we can see that the overall
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RMS accelerations are higher in case of bearing 2 (away from the motor) as compare the bearing 1 (near to the motor) in all the fault analysis. 11-References:[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Beatty R.F., ,” Differentiating Rotor Response due to radial Rubbing.”Jl. Of Vibration Acoustics, Stress and Reliability in Design, 1985, pp151-160. Emmanouilidis, C, MacIntyre, Dr. J., Cox, Prof. C., , “Neuron fuzzy computing aided machine faults diagnosis”, Rroc.of JCIS’, The Fourth joint conference on information sciences. Research Triangle Park, North Carolina, USA, 1998, Vol 1. pp 207-210. Vyas, N.S. and Satish Kumar D., , “Artificial Neural Network design for the fault identification in a rotor bearing system”, Mech. And Mach. Theory, 36, 2001, pp157-175. Srinivasan, K.S. “Fault diagnosis in rotating machines using vibration monitoring and artificial neural network”, Ph.D Thesis, ITMMEC, IIT Delhi 2002. Adewasi S.A, B.O.Al. Bedoor.”Detection of propagating cracks in rotor using neural networks” Pipe and component Analysis and Diagnosis, 2002, PVP-Vol, 447, Kalkat M, S. Yildirim and I. Uzmay., “Rotor dynamic Analysis of Rotating machine system using Artificial Neural Network”, International Journal of Rotating Machinery 9,2003, pp255-262 Kashyap, P.K. “Application of ANN for the fault Diagnosis of rotor System”, M.Tech Thesis, ITMMEC, IIT Delhi, 2005, Hakim Enayet, “Experiment design for simulation different faults in a rotorkit”, www.ualberta.ca/~slshah/public_share/ehalim/Experiment%20Design%20%20%20Rotor%20Kit.pdf,2005, Sanjin SC. BRAUT, Doc.Dr.sc. Roberto ZIGULIC, Ante SKOBLAR DIPL.ING, Prof.Dr.SC, mirko BUTKAVIC.,“Model Testing of rotor dynamic Test Rig for Rotor- Stator Rub Investigation”.Monticelli Terme/ Parma-Italy, 2005. Travis Joel Bash.,“Active Magnetic Bearings used as an Actuator for Rotor Health Monitoring in Conjunction with Conventional Support Bearings”, Master of science in mechanical engineering Thesis Virginia Polytechnic Institute and State University,2005. Bhandari V.B, “Design of Machine Elements”, Tata McGraw-Hill Publishing Company Limited New Delhi, 2004, pp234-237. Grover G.K,”Mechanical Vibrations”, Nem Chand &Bros., Roorkee, India, 2003, pp333-345. Ghosh and Mallik, “Theory of Mechanisms and Machines”, East-West Press Private Limited New Delhi India pp 290-293.
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