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Static and Modal Analysis of Jeffcott Rotor Under Low Volume
Conditions
Veeresha kallamat1, Dr. K M PURUSHOTHAMA2
1Student,
Master of Technology, Dr. Ambedkar Institute of Technology Bangalore, Karnataka, India
Dept. of Mechanical Engineering Dr. Ambedkar Institute of Technology Bangalore, Karnataka, India
----------------------------------------------------------------------***--------------------------------------------------------------------2Professor,
Abstract - A thermal power station is a power plant in which the prime mover is steam driven. Here the work is focused on the
study of behavior of steam turbine rotor in low volume flow condition with the rotor dynamics concept using ansys. The
Jeffcott rotor is modeled by pro-e modeler, meshed and analyzed by ansys workbench. In this paper we described the design
and analysis of single stage Jeffcott rotor and multistage Jeffcott rotor. Further comparison of standard single stage rotor with
modified single stage rotor of equivalent stresses, maximum principal stresses and total deformation again comparison of
standard multistage rotor with modified multistage rotor’s stresses and total deformation. The0analysis results are
tabulated0and found that during normal0operation the stresses are within0the allowable limit but in low0volume flow
condition the stresses0are exceeding the allowable0limit. Reduction in weight0of rotor without affecting the0functionality
and efficiency0of turbine will help to reduction0in material cost, weight0etc.
Key Words: Steam turbine, Jeffcott Rotor, Static and modal analysis, Equivalent stresses.
1. INTRODUCTION
The majority0of the conventional0power generation is0associated0with the consumption of
natural0resource0and are not0sustainable.This has led to a growth0in renewable and localised0production of power,
which is expected0to address all these0problems.This diversificationnof power0generation method has enhanced the
requirement0for operational flexibility0of steam turbines in power0production. Renewable energy0sources cannot
provide0uninterrupted and reliable0power production as0their output is often difficult0for predicting and
storage0capacity is also not available in the required0quantities.These results in large0variations of the power0demand
from conventional0power production.steam0turbines are increasingly0expected to be operated in regions0without
sufficient0water-cooling such as desert0regions. A steam0turbine is a heat0engine in which the0energy of the steam
is0transformed into work. First, the0energy in the steam0expands through a nozzle and is converted0into kinetic0energy.
Then, that kinetic0energy is converted into work on rotating0blades.The turbine0is divided into0different modules with
the
different0pressure
levels.
The0critical
components
in
terms0of
flexible0operation
are
those
enduring0highertemperature and higher pressure0such as the inlet0valves or the rotor of the high
andintermediate0turbine, which can suffer from0low cycle fatigue under0high thermal transients.
Causes0of Failures in Industrial0Turbine
Following are0the major causes of failure0of industrial0turbines.
1.
Weight0Unbalance
2.
Bearing0misalignment
3.
Resonance0(Critical Speed)
4.
Centrifugal0forces
5.
Uneven loads0on rotor.
LITERATURE SURVEY
Dilip Kumar Garg, Shrinivas Chambalwar, Jayant Sarode and0Ajay Dhanopia et.al., [1] presented the
rotating0instability flow0phenomenon numerically in the0last stage of0low pressure steam turbine0operated at very0low
mass flow0rate. This kind0of instability0imposes a0major risk0to the0mechanical stability of0last stage moving
blades0in low pressure0steam turbines. Goal0is to predict0the unsteady flow0phenomena and0their effects.
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Nagaraju Tenali10and Srinivas Kadivendi1et. al., [2]worked on analysis of0steam turbine rotor0using Rotor
dynamics0principles. . Rotor dynamics Mainly0deals with0studies of0lateral and0torsional vibrations0of rotating shafts
or0structures with the main0objective of predicting0rotor vibrations0and limiting the vibration0level under
an0acceptable limit. The generalized Jeffcott rotor0consists of long flexible0mass less shaft0with flexiblebearings0on both
the ends. The different0analysis carried0out to the rotor dynamic0integrity of the steam turbine rotor such0as Modal
analysis, Harmonic0analysis and Transient analysis in Ansys.
Chenchu0Deepa, B.Jayachandraiahet. al., [3] conducted an analysis to estimate the Efficiency of Low Pressure0Steam
Turbine. The steam0turbine blade performance0is related to many0factors. One of the important factors is the
change0and degradation in turbine0blade profile after many0operations. This leads to increased0in flow losses and
hence0reduction in overall efficiency0of turbine. The performance0of turbine blade can be predicted and improved0by
using Computational0Fluid Dynamics (CFD).
PROBLEM DESCRIPTION AND OBJECTIVE
The objective0of this study is to study0the behavior of steam0turbine rotor in low volume0flow state in LP stage0by
applying0rotor dynamics0concepts.
Following stages are followed by
1.
Initially0simple Jeffcott rotor0will be0studied in order to understand0the dynamic behavior of such0simple
rotors before0dealing with large0industrial rotors.
2.
3.
The study0will include predicting0critical speeds calculation0for Jeffcott rotor.
After the study on the Jeffcott0rotor model, a finite0element model of a Jeffcott0rotor will be meshed0and
formulated in ANSYS0software.
Critical0speedis calculated mathematically0for single stage rotor.
4.
5.
Static structural0analysis module is0used to calculate0displacements, strains, stresses and reaction0forces
under the effect0of applied loads.
6.
By plotting0Campbell diagram with the results0from Modal analysis, critical0speed is verified and
compared0with the calculated values.
METHODOLOGY
1.
2.
3.
4.
Involves0behavior of single0stage rotor (Jeffcott0Single Mass0Rotor) and analyze
by0mathematically and also by analytical0method by using0 Ansys.
Study of0change in frequency0of the rotor as the0mass & speed of rotor0varies.
Study of0behavior of single0stage rotor in various0operating speeds0and frequencies.
Study of critical0speed and resonance of single0stage rotor and plotting0Campbell diagram.
the
results
Finite Element0Approach
The process0of data analysis0proceeds in two stages:
a.
Identifying the0appropriate type of0model (with
viscous or structural0damping). This choice is often in
practice0limited by software0used for the modal0analysis. Most of software0packages work with one type
of0damping and give no choice0to the user.
b.
Determining0appropriate parameters of the
chosen0model. This stage, also0called modal
parameters0extraction, is done by0curve-fitting of the measured0frequency response0functions to the
theoretical0expressions.
Material Selection
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Material
ChromeSteel(X28CrMoNiV49)
Density
7.7x10-9Kg/mm3
Young's0modulus
2.1x105 MPa
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Volume: 06 Issue: 09 | Sep 2019
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Yield strength at room temperature
550 MPa
Yield strength at 1000 temperature
540 MPa
Poisson's0ratio
0.3
FOS at 100% operating Speed
1.68
FOS at 121% operating Speed
1.15
Allowable stress at 100% operating
Speed
FOS at 121% operating Speed
321MPa
469MPa
Geometric0Modeling
3D model of Jeffcott’s Rotor
3D model of Modified0Jeffcott’s Rotor
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Description
Jeffcott Rotor
Modified Jeffcott Rotor
Length of Rotor0Shaft
1.5 m
1.5 m
Dia. Of0Shaft
0.2 m
0.2 m
Dia. Of Rotor0Disk
0.5 m
0.5 m
Thickness of0Rotor Disk
0.05 m
0.05 m
OD of Cutout in Disk
0.50m
0.425m
ID of Cutout in Disk
0.30m
0.275m
Thickness of Cutout in Disk
0.007m
0.005m(Both Sides)
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Meshing
Meshed0model of the Multi Stage Rotor
Meshed model of the Modified0Multi Stage Rotor
RESULTS AND DISCUTION
The figure 6.1shows0Equivalent stress of 291.45MPa for the singe stage0rotor with rotational velocity of 6500rpm and
displacement.
The figure 6.2 shows total0deformation of 0.150 mm for the rotor with the rotational velocity of 6500rpm
and0displacement.
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The figure shows Maximum Principal Stress of 0.1363 mm for the rotor0with the rotational velocity of 6500rpm
and0displacement.
Description
Singe Stage Rotor
Modified Singe Stage
Rotor
Equivalent Stress(Von
Mises) in Mpa
291.45
265.05
Maximum Principal
Stress in Mpa
364.7
331.97
Total deformation in
mm
0.1363
0.1506
Mode 1
The figure shows total0deformation of 2.3428 mm in first
boundary conditions
mode with the0frequency of 221.05 Hz for the given
Frequency and Deformation of Standard Jeffcott’s Rotor
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Mode
Frequency in Hz
Deformation in mm
1
221
2.34
2
784
3.5933
3
1490
12.364
4
1680
7.37
5
2301.5
15.043
6
4965
25.291
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The figure shows total0deformation of 2.3428 mm in sixth mode with the0frequency of 4965 Hz for the given
boundary conditions.
Frequency and Deformation of Modified Jeffcott’s Rotor
Mode
Frequency in Hz
Deformation in mm
1
209.9
2.322
2
758.98
3.83
3
1341.9
12.995
4
1627
7.466
5
2008.3
18.558
6
4430.7
31.243
Comparison of Stresses and0deformation
Standard Multi Stage Rotor
Modified Multi Stage Rotor
Equivalent Stress in Mpa
224.76
253.59
Maximum Principal
Stress in Mpa
340.57
407.5
Total deformation in mm
0.4245
0.34485
CONCLUSIONS
The0main objective of the work is0focused on the study of behaviors0of steam turbine rotor0in low volume flow
condition0with the Rotor Dynamics0concepts using Ansys. Here0the basic work involved0is study of single stage
(Jeffcott's) rotor0and the results0are compared with0multi stage steam0turbine rotor. Here we mainly0concentrated on
Low Pressure0stage turbine experiences0stresses due to low volume0flow.
The0Multi stage steam turbine0rotor is modeled in Pro-e0and meshed in ANSYS 14.5 Workbench. A0methodology
to determine dynamic0stresses of low pressure0stage steam turbine0rotor under low volumetric0flows of steam is
illustrated. Stresses0are tabulated and mode0shapes with deformation at0certain speed is plotted and0are evaluated
from0centrifugal load or speed0from a static structural0analysis module and the0results tabulated in table 6.4 shows0the
deformation and stresses0generated in the Multi stage0steam turbine rotor and0are within the acceptable0limit.
REFERECES
[1]
Dilip0Kumar Garg, Shrinivas Chambalwar, Jayant0Sarod and Ajay0Dhanopia, “Investigation of0Rotating
Instability0in the Last Stage of0Low Pressure Turbine during0Low volume flow0Operation.” International
Journal0of Recent advances in Mechanical0Engineering,pp 143-147 Vol.4, No.2, May 2015.
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[2]
Nagaraju0Tenali and Srinivas0Kadivendi, “Rotor0Dynamic Analysis of0Steam Turbine Rotor0using Ansys.”
International0Journal of Mechanical0Engineering and Robotics0Research, pp-124-126Vol. 3, No. 1, January 2014.
[3]
L. Tajč, L. Bednář, and0M. Hoznedl, “Flow0conditions in the last0stage during idling operation0and low output of
1000mw0turbine.” 18th International0Conference of Engineering0Mechanics, pp. 1353–1361, Paper #31, May
2012.
[4]
Mohini0R. Kolhe1, Prof. A. D. Pachchhao0and Prof. H.G.Nagpure,“Thermal0Stress Analysis In0Steam Turbine
Rotor -0A Review.”IOSR Journal0of Mechanical and Civil0Engineering (IOSR-JMCE) e-ISSN: 2278-1684, p-ISSN:
2320-334X, PP 83-86, 2014.
[5]
C. Chattoraj, S.N.0Sengupta and M.C. Majumder, “Analysis0of Dynamic Behaviour a0Rotating Shaft with
Central0Mono-Disk.” International0Journal of Engineering0& Technology0Research, Vol-1, Issue-1, July–Sept2013.
[6]
Mili J. Hota and0D.P. Vakharia, "A Review0of Rotating Machinery0Critical Speeds and0Modes of Vibrations."
International0Review of Applied0Engineering Research, Volume-4, Number 3-2014.
[7]
Manjunath H S, Sharath kumar S.N. Mahesh prasad L, Dr. Sathish S “structural and vibration analysis of propeller
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November- 2018. PP 595-600
[8]
A Chenchu0Deepa, B.Jayachandraiah, "CFD Analysis0for Estimation of0Efficiency of Low0Pressure Steam
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Issue-3, August 2012.
[9]
N. Lenin0Rakesh, V. Palanisamy0and S. Jeevabharathi, “Stress0Analysis of a0Shaft Using0Ansys”, MiddleEast0Journal of Scientific0Research 12 (12): 1726-1728, 2012.
[10] Ge0Li-juan, Zhang0Chun-hui, Hao Min, Zhang0Yong, “Vibration0Analysis of the Steam0Turbine Shafting caused by
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[11] J.S. Rao and0K.Ch. Peraiah, “Estimation of0Dynamic Stresses in Last0Stage Steam Turbine0Blades under Reverse
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