Experimental Technique for Diagnosing Fractures in Shaft Lines Applied to a ROV
Supply Vessel
Severino Fonseca da Silva IMeto, Luiz Antonio Vaz Pinto and José Marcio do Amaral
Vasconcellos
COPPE & Escola Politècnica / Federal University o f Rio de Janeiro, Brazil. Corresponding author: jmarcio@peno.coppe.ufrj.br
Abstract
The paper presents an experimental technique used f o r fracture diagnostics o f ship shaft Unes including the development o f a data acquisition and signal processing system. The investigation aims to determine the effect o f forced vibrations. Experimental and theoretical studies were carried o u t on a tug-type vessel. Experimental data associated ivith expert system programs to calculate alignment and dynamic behavior o f discrete systems using the f m i t e element m e t h o d that makes i t feasible to i m p l e m e n t recommendations to minimize the shaft line vibration level. The objective is to avoid the occurrence o f structural failure
Keywords
V i b r a t i o n , propeller shaft, shaft alignment
1 Introduction
Small-sized vessels normally use propulsion engines o f m e d i u m and h i g h rotation speeds to ensure economy and efficiency i n performance. I n t u r n , these engines together w i t h other equipment installed i n the propulsion system, induce forces i n the shaft line. These forces are harmonic w i t h multiples source frequency f o r the operating equipment. Each equipment and structural component, i n t u r n , have its own natural vibration frequency.
The p r o x i m i t y between the frequencies can excite the hull structure or the coupled equipment. This can cause a loss o f efficiency, a reducfion i n the maintenance period, or even structural failures and increasing costs. A problem o f forced vibration o f one o f t h e elements o n board can generate high repair costs, jeopardizing even the economic viabihty o f the vessel. W i t h the aim o f investigating the effect o f forced vibrations, experimental and theoretical studies were carried out o n a tug-type vessel.
The tug boat selected was converted into a ROV (Remote Operated Vehicle) Supply Vessel. The tug includes two m a i n engines and two shaft lines f o r fixed-pitch propellers. I n the conversion process, the propellers were replaced by a controllable-pitch propeller type and propulsion shaft lines were replaced by a hollow shaft and an O.D.Box (oil distribution box) f o r activating the controllable-pitch mechanism. A f t e r the modification f o r period o f approximately t w o years, the vessel experienced successive fractures i n the shaft lines ( o n b o t h sides), w i t h a total o f 5 damages.
I n each location, acceleration was measured i n three directions (vertical, horizontal and axial). The measurements were made d u r i n g engine operation f o r d i f f e r e n t speeds. D u r i n g the measurement phase the rotation speed signal was acquired through a magnetic p r o x i m i t y sensor installed o n each shaft.
A n experimental procedure used f o r the fracture diagnostics in the shaft lines was supported by the development o f a data acquisition and signal processing system based on virtual instruments i n L a b V i e w T M software [ N . I . , 1998].
D u r i n g the tests, o i l w h i r l , resonance, static misalignment a n d w h i r l i n g were i d e n t i f i e d . T h e y were c o n f i r m e d b y numerical models, making possible the recommendation o f measures to minimize the vibration effects which cause fracture o f the shaft lines.
2
Theory of Shaft Vibration
I n crankshafts o f complex geometry, the c o u p h n g effect bettveen torsion, bending and axial forces can be considered. I n general, torsional modes of vibration are coupled w i t h out-of-plane bending modes whereas axial modes are coupled w i t h in-plane bending modes.
Drawing o f a tug line shaft is presented i n Figure 1.
Fig. 1 Tug shaft line [MACHADO et al, 2004]
Kinetic and potential energies Tand Vof a continuous system and the w o r k IF done by the forces w h i c h act o n it are related as shown i n Equation 1, as stated b y Hamilton's Principle [ C L O U G H and PENZIEN, 1975]:
S\(T-V) + \SW = Q (1)
A finite element model i n which the continuous displacement variables ti, , iiy , ii, and r o t a t i o n variables 0^, 6,., 0^ i n a rectangular Cartesian coordinate system (x, y, z) presented i n Figure 2 may be substituted into interpolated nodal variables Ul t o obtain the Lagrange equations (Eq. 2):
d
' sv'
(Il dter ^ SV _^ SUi Su,
where F; are the generalized forces.
(2)
Fig. 2 Finite Element Coordinate System [DYKSTRA, 1996] A d d i n g the kinetic energy o f translation, given by (Eq. 3):
r , = f ( v . v ) = f b - o ^ O ' > y H - ) i (3)
w i t h the rotational kinetic energy o f the element about its center o f mass, where small angle approximations have been made, and integrating over the element length L, yields (Eq. 4):
dill/ \ dm ^ x 2 , , . 2 ,
(4)
I n E q u a t i o n 4, J, a n d Jt„ t e r m s c o r r e s p o n d t o the p r i n c i p a l d i r e c t i o n s o f the i n e r t i a tensor [J] d e f i n e d per u n i t l e n g t h .
Elastic potential energy or strain energy is defined as a function of stress {a} and strain {e}, obtained per unit voliune as indicated i n Eq. 5:
Vi = i{H.d{s})=\{{sY[K,]{s})
(5)where [ATi] is the elastic matrix that correlates stress and strain in the generaUzed version o f Hooke's Law (Eq. 6):
(6)
For Young modulus E, area A , transversal elasticity m o d u l e G, moments o f inertia 1 , , l y , , the total energy is obtained by the integration over the volume [DYKSTRA, 1996]. The terms F, and represent linear contributions; F, due t o the axial load and torsion and V^ due to bending (Eq. 7 a n d 8):
EA-2 • Sux GI f (S0^ 2 Sux dx + ^ \ dx Sx 2 •' dx . \ ) 2 •' K J
f f
EI i ^80, dx+^\ dx 2 { dx ) V J\
) dx (7) (8)E x p e r i m e n t a l T e c h n i q u e f o r D i a g n o s i n g F r a c t u r e s in S h a f t L i n e s A p p l i e d t o a R O V S u p p l y V e s s e l Severino Fonseca da Silva Neto, Luiz Antonio Vaz Pinto and José Marcio do Amaral Vasconcellos
C o u p l i n g s can be observed t h r o u g h the n o n - l i n e a r contributions (Eq. 9):
{//} = {(t)}5/«(co/) (15) where { 0 } and represent, respectively, the eigenvector
(vibration mode) and the eigenvalue o f the free vibration equation (Eq. 16):
due to the axial/bending couphng Vj (Eq. 10):
bending/axial coupling F, (Eq. 11):
2 J a r V a v / 2 j a v V a , / axial/torsion (Eq. 12):
and torsion/bending (Eq. 13):
_ ( g - G ) / / f j e , g (13) 2 { 8x ' dx
A discrete system o f d i f f e r e n t i a l equations o f d y n a m i c equilibrium is finally given as (Eq. 14):
Precise d e t e r m i n a t i o n o f the l i n e a r a n d / o r n o n - l i n e a r parameters w h i c h represent the stiffness m a t r i x [K] based on the elastic potential energy and o f mass [M] based on the kinetic energy o f the system, modeled using the f m i t e element method, as well as the vector o f the external forces \f(l)] and the d a m p i n g m a t r i x [ C ] , allow the d e t e r m i n a t i o n o f the numerical solution o f the system o f differential equations, where the vectors |/V}> {»} and correspond, respectively to acceleration, velocity and displacement.
D i r e c t i n t e g r a t i o n o f E q u a t i o n ( 1 4 ) , b y a step-by-step procedure includes the nonlinear coupling stiffness f r o m the displacements.
A n o t h e r type o f analysis that sheds m o r e l i g h t o n the dynamic behavior o f mechanical systems is the study o f f r e e u n d a m p e d v i b r a t i o n s . T h e greatest d a m a g e t o m e c h a n i c a l systems is g e n e r a l l y caused by resonance c o n d i t i o n s , w h i c h o c c u r w h e n t h e f r e q u e n c y o f the excitation force is close to the n a t u r a l frequency CO (rad/s) o f t h e structure. Supposing that [ C ] = [ 0 ] and \f(0}={0], the f o l l o w i n g s o l u t i o n is proposed (Eq. 15):
[ A : ] { ( ( . } = a ) ^ [ M ] { , t , } (16)
For the solution of the eigenvalue problem and the calculation o f the overall problem o f forced vibration, i n the time and f r e q u e n c y d o m a i n s , i t is essential to have a c o r r e c t representation of stiffness, structural mass, adjacent fluid mass and, particularly, damping and force, generally obtained by means o f f u l l scale measurements.
Another characteristic o f crankshafts o f complex geometry is related to the coupling o f the strain on orthogonal planes, produced b y any asymmetry o f the moment o f inertia o f the X Z and X Y planes. This asymmetry produces cross coupling in the movement o f the shaft (when deformed o n the X Z plane, a moment appears which tends to rotate i t towards the X Y plane - o f less stiffness). This m o m e n t is o f a sinusoidal n a t u r e , w h i c h i n t r o d u c e s a n o n - l i n e a r i t y i n the s h a f t movement equation that can be depicted i n a simplified way through the "Mathieu" equation [ M E I R O V I T C H , 1975). This phenomenon is called a parametric vibration and can also be responsible f o r generating a classic situation o f rotordynamic instabihty This is known as parametric instability and generates sub-harmonics ( n o r m a l l y at a frequency equal to half the rotation speed) i n the shaft m o t i o n .
3
Propulsion Shaft Line
3
.1 Propeller Shaft Alignment
3.2
Torsion Propeller Shaft Vibration
Torsion propeller shaft vibration i n a ship is caused by the torque variation due to the irregular blades water f l o w and by the forces generated by the gases i n the cyhnders, as well as the unbalanced masses i n the system. Excitation frequencies are in general equal to the rotation speed of the system multiplied by the number o f propeller blades, or by a multiple number. They can also depend on the number o f engine cylinders, the order o f f i r i n g , or whether i t is a Uvo or four-stroke engine.Calculation o f t h e natural frequencies o f torsional vibration of the shaft line is i m p o r t a n t f o r determining the propeller shaft critical speed. One method o f modeling the shaft line is based o n its transformation into a system o f torsional discs and springs, the theory of which is based on Holzer's method [ M E I R O V I T C H , 1975].
3.3
Propeller Shaft Axial Vibration
Propeller shaft axial or longitudinal vibration is caused by the propeller due to the thrust pulsations or the forces o f the gases i n the m a i n engine. I n this case the excitation frequency w i l l be the m u l t i p l i e d b y the number o f propeller blades, or a multiple o f this. The number o f cylinders i n the main engine also exercises some influence.
Axial natural vibration frequency o f the propulsion system, including the crankshaft, propeller and intermediary shafts lies in the 500 to 800cpm band. Possible occurrence o f a resonance condition exists, w i t h components o f fifth to seventh order, i n the variation o f the pressures on the pistons i n the engine cyhnders, f o r a normal rotation speed i n the 110 to 200 r p m range. I t is w o r t h remembering that in this type o f vibration, there is also a contribution from the propeller thrust fluctuation, as has aheady been seen, and i t occurs at the blade frequency.
W h e n there is an axial vibration resonance i n the propulsion system, the longitudinal excitation force (forward and reverse) is transmitted to the h u l l structure and superstructure, and i t is amplified due to the propulsion system. As a consequence, an excessive vibration o f the superstructure occurs.
To describe the axial vibration mechanism o f the crankshaft, we need to consider its i n i t i a l causes, which are listed below: • variation of the propeller thrust
• variations i n the explosion pressures o f the cylinders • torsional vibration of the propeller shaft, producing
warping o f the sections.
Calculation of the propulsion natural frequencies can be made by means o f modeling equivalent masses and springs. Natural frequency o f the longitudinal vibration of the propeller shaft, of which the crankshaft is an integral part, depends mainly o n the propeller mass (including, the virtual mass), the spring constants o f t h e crankshaft and the thrust bearing. Equivalent stiffness o f the t h r u s t b e a r i n g can be calculated as a n association i n a spring series that represent t w o components.
One o r i g i n a t i n g i n the thrust collar and the other i n the thrust block.
The influence o f the shaft torsional vibration o n the axial vibration, is very small. This is because o f the d i f f i c u l t y o f an engine to be w o r k i n g at a rotation speed that corresponds to or is close to the natural frequency o f the torsional vibration. I n cases o f torsional resonance, the warping o f the sections w i l l produce contractions and distensions i n the shaft i n the axial d i r e c t i o n , c o n t r i b u t i n g m o r e s i g n i f i c a n t l y t o the longitudinal vibration o f t h e propeller shaft.
3
.4 Lateral Vibration and Shaft Whirling
The propeller can cause w h i r l i n g , or rotation o f the bending plane, and the lateral vibration o f the propeller shaft, when the hydrodynamic forces i n the blades suffer variations, due to the wake field. The excitation frequencies are the same as indicated i n the previous sections.
4 Experimental Technique
Data obtained expermientally [LOPES et al, 1986] helped to determme the dynamic behavior o f the main engine/structure interaction [LEGUE et al, 1990] and the propulsion shaft line stiffhess/ship hull flexibihty interaction [ M A C H A D O et al, 2004].
A better understanding o f the machine vibration [LOPES et al, 1985],structure vibration causes [SILVANETO etal, 1996], a n d an access t o the actual values o f t h e i r parameters
[ D O M E N I C O et al, 1997], obtained experimentally, leads to the improvement i n the quaUty o f design and construction processes [ M E L L O et a l , 2 0 0 6 ] . The a b i l i t y t o simulate satisfactorily the actual behavior through an adjustment of the models to the experimental data, verifying and proposing measures for minimizing vibration, contribute to avoid damage to the floating system, environment and human life.
4.1 Experimental Data IVlanager
The data manager was conceived [NOVAES et al, 1999] to allow the electric signals obtained from mechanical-magnitude sensors to be introduced through keying i n (RMS total values or by octave band).
The m a i n data-management modules have the f o l l o w i n g characteristics:
a) Storing general i n f o r m a t i o n o f the ship, sea trials, sea and o p e r a t i o n c o n d i t i o n s , mechanical e q u i p m e n t and / o r evaluated structure.
b) Managmg information about the electronic mstrumentation parameters (channel, attenuation, sampling rate etc.) and i t s a s s o c i a t i o n w i t h the m e c h a n i c a l data o f i n t e r e s t (conversion factor between volts and the desired engineering u n i t ) .
E x p e r i m e n t a l T e c h n i q u e f o r D i a g n o s i n g F r a c t u r e s in S h a f t L i n e s A p p l i e d t o a R O V S u p p l y V e s s e l Severino Fonseca da Silva Neto, Luiz Antonio Vaz Pinto and José Marcio do Amaral Vasconcellos
c) C a r r y i n g o u t the data a c q u i s i t i o n and the signal p r e -processing.
d) Selecting the analysis domain (time or frequency). e) Analyzmg the signals through Fast Fourier Transform (FFT),
direct comparison w i t h norms, event statistics or cascade diagrams.
f ) Storing final results, allo^ving fiUure access and comparisons w i t h similar problems and respective solutions.
4
.2
Data Acquisition
Acquisition module allows to introduce data through keying i n , n u m e r i c a l f i l e r e a d i n g or d i r e c t l y , f r o m the signal conditioner (filter/ amplifier).
The pre-processing signal module (Fig. 3) makes i t possible to treat the signal acquired through filters and amplifiers. A Fourier analysis can also be performed, t r a n s f o r m i n g the discrete signal obtained i n the tune domain to the spectrum. Electric strain-gages mstalled at 45 degrees to the shaft line and connected i n a Wheatstone Bridge enables one to measure the shaft strains and, consequently, torque, torsional vibration and shaft horsepower (SHP). Through telemetering (frequency modulated by the torque), the signal is sent by a transmitting antenna to a discriminator coupled to the database by means of an analogue-digital board.
The signals are then processed, stored and presented i n the f o r m o f torque, torsional v i b r a t i o n and power w i t h the additional reading o f a pidse at each shaft rotation.
Piezoelectric accelerometers coupled to magnetic bases record the local vibration through portable recording equipment or directly i n the data manager, where the processing allows a direct comparison w i t h acceptable limits proposed by the norms (Figure 4).
licr^ ISO 26Jt ; Vat-i't^f.
Fig. 3 Comparison with Limits Acceptable by ISO and Bureau Veritas
The same modules responsible f o r the a c q u i s i t i o n and processing o f local vibration signals can be used f o r measuring mechanical equipment vibration.
Analysis o f equipment vibration, however, requires more than one type o f numerical signal treatment.
The main engine, when new has a dynamic behavior different f r o m when i t is installed i n the ship machinery space. Figures stored i n the data manager show the model of a motor vibrating i n its natural modes T or H (transversal / horizontal), X (forward and reverse out o f phase) and L (longitudinal), i n the factory and i n the ship (machine / h u l l structure coupling).
Equipment vibration during the critical speed can be analyzed simultaneously i n time and frequency domains, as indicated i n Figure 4.
The data manager also allows spectra o f the same p o i n t o f the machine to be presented i n three orthogonal directions, f a c i h t a t i n g the diagnostic o f possible p r o b l e m s [LOPES et al, 2 0 0 2 ] .
Fig. 4 Analysis of Passage through Critical Rotation Speed -Time and Frequency
Cascade diagrams are used d u r i n g machine stop or start up (Figure 5 ) . D i f f e r e n t spectra o b t a i n e d sequentially are presented together, making possible to i d e n t i f y a possible resonance condition.
C w i M • C u t M r
S18 ooo
Fig. 5 Cascade Diagram for Machine Stoppage Test
1 X rotation speed: • Unbalance
• Misalignment or warping o f the shaft • Tensioning
• Loose components • Resonance • Electric
2 X rotation speed:
• Misalignment or warping o f the shaft
H a r m o n i c :
• Loose components • Friction
Sub-harmonic: • O i l W h i r l
• BaU bearing retainer
N e t w o r k multiple: • Electric
Resonance:
• Different sources, including shaft, carcass, foundation and external structures, frequency proportional to stiffness and inverselyproportional to mass.
Rotation speed multiples: • Defective bearings • Gearing • Drive belts
• Blades and diaphragms
Fig. 6 Fracture in the Propeller Section
At the end o f November 2005, two programs were carried out for measuring the vibration i n four points o f the 2 shaft lines. Figure 7 shows a drawing o f the shaft line and the 4 points where the v i b r a t i o n signals were required, i n Axial, Vertical and Transversal directions.
Afl Stem Tuba
Aliaad Slem Tube
Fig. 7 Drawing of the Line shaft
Vibration signals were acquired w i t h the RSV vessel anchored at the port and w i t h the engines at a rotation speed o f 471 r p m . The forces and moments o f unbalancing inherent to the engine constitute the m a i n source o f excitation o f the system. I t is k n o w n that the moments o f a first order ( M l v ) and second order ( M 2 v ) are transmitted to the structure o f the vessel and then to the shaft line bearings, particularly f o r engines o f 4, 5 and 6 cylinders. I n this case, the structure is excited according t o the data shown i n Table 1.
Right at the outlet o f the engine there is the r e d u c t i o n box (3:1). The excitation frequencies, at the p o i n t o f operation o f the engine, after the r e d u c t i o n box, are also shown i n Table 1.
5 Case Study - Salgueiro Vessel
Salgueiro vessel, originally a t u g vessel, was converted to a RSV ( R O V Supply Vessel) i n 1994. The tug h a d 2 m a i n engines and 2 line shafts f o r fixed-pitch propellers. I n the c o n v e r s i o n process, the p r o p e l l e r s were replaced b y a c o n t r o l l a b l e - p i t c h type, the p r o p u l s i o n shaft lines were replaced by a h o l l o w shaft and an o i l d i s t r i b u t i o n box was introduced f o r activating the controllable-pitch mechanism ( C D . B o x ) . Since then, over periods o f approximately 2 years, the RSV vessel suffered successive breaks i n the line shafts (at the 2 edges), totaling 5 damages. Figure 6 shows the fracture o f the last damaged shaft.Table 1: Points o f Engine Operation
Excitation
Frequencies
Value Before
Reduction Box
(Hz)
Value After
Reduction Box
(Hz)
1X
7,8
2,6
2X
15,7
5.2
6X
47,1
15,7
I n the analyzed spectra, the vertical lines indicate the 1", 2"'', 3"', and so f o r t h , vibration frequencies i n the shaft after the
E x p e r i m e n t a l T e c h n i q u e f o r D i a g n o s i n g F r a c t u r e s i n S h a f t L i n e s A p p l i e d t o a R O V S u p p l y V e s s e l Severino Fonseca da Silva Neto. Luiz Antonio Vaz Pinto and José Marcio do Amaral Vasconcellos
reduction box. The notation that w i l l be used to denote these frequencies w i l l be: the 1st frequency denoted by I X , the 2"'' f r e q u e n c y b y 2 X , the V' f r e q u e n c y by 3 X ; and so o n successively.
The measurement was carried out at four points o f the shaft line. Figure 8 shows the RSV vessel main engine, which is a V8 BSiW engine. The accelerometer was positioned i n the engine block, at the t i p o f the engine flywheel.
Fig. 8 Point 1 - Engine Port
At about 1 meter f r o m the reduction ouriet, the line shaft penetrates a bulkhead (Figure 9 t o p - l e f t ) , w h i c h divides the ship's engine r o o m . Right after that, one o f the intermediary bearings is located.
Figure 9 t o p - r i g h t shows the second intermediary bearing (Point 3).
Fig. 9 Points on Port: #2 ( 1 " intermediary Bearing), #3 (2"' Intermediary Bearing), O.D. Box and #4 (Stuffing Box)
B e f o r e r e a c h i n g the s t u f f i n g b o x , r i g h t a f t e r t h e 2"'' intermediary bearing, another accessory o f the shaft line is located: the o i l distribution box (O.D. Box), seated on pads, produces large-scale vibration. This equipment weighs 1,150 kg and is shown i n Figure 9 - bottom-left.
Finally, the shaft line penetrates the bulkhead, which separates the Engine Room from the Stern Tube area. Figure 9-bottom-right shows the S t u f f i n g Box. The ring that appears i n the lower right corner is f o r distributing the lubricating oU.
For each of the four points, measurements were made on each side (Port or Starboard) and i n the three dkections (V=vertical, T=transversal, A=axial), thereby obtaining 6 spectra f o r each point, making a total o f 24 spectra per program. Figures 10 and 11 show the vibration spectra obtained f o r p o i n t 2, i n the port shaft, i n the vertical direction, i n the first and second programs, respectively.
10 15 20 25 30 35 40 « 50 rrequency 1H21
Fig. 10 Vibration Spectrum - Point 2V - Port - 1" Program
Vibration Spectrum - Point 2V - Port Program
Analysis o f the obtained spectra indicates the f o l l o w i n g diagnosis:
• Oil W h i r l : peaks o f velocity beUveen 0.43 and 0.48 x RPM; • Peaks o f v e l o c i t y i n the 6 X frequency, at the p o i n t 2,
starboard, indicating resonance: lateral frequency (whirUng) of the shaft (between intermediary bearings) coinciding w t h an excitation frequency o f the engine (2""' order); • The p r o b l e m o f m i s a l i g n m e n t is m a r k e d b y large-scale
vibration i n the 2X frequency, together w i t h a high level o f axial v i b r a t i o n . The v i b r a t i o n peaks i n the 2X frequency are present i n almost all the spectra and the axial vibration of the r e d u c t i o n b o x has a peak value o f about 2 m m / s , w h i c h can be considered h i g h , w h e n axial v i b r a t i o n is evaluated;
• For the same measured p o i n t (e.g. p o i n t 4 ) , same engine load (80%), same direction (vertical) i n the starboard and port shaft line, one can observe a similar aspect i n the spectra, although w i t h greater vibration level f o r the port shaft line, w i t h a controllable pitch system.
6 Comparison with Numerical
Models
Two numerical models o f the shaft line were built: one for ahgnment analysis and the other composed by f m i t e elements f o r free vibration analysis (natural frequencies and vibration modes). I n b o t h cases, the shaft line was subdivided i n t o 73 s e c t i o n s , r e p r e s e n t i n g i t s g e o m e t r i c a n d m e c h a n i c a l characteristics.
The results obtained from the alignment calculation were the reactions i n the bearings (Figure 12), the influence matrix (Figure 13), the elastic line (Figure 14), shear force diagram (Figure 15) and bending moments (Figure 16).
Bearing number
1 2 3 4 5 É
2247,1 930,0 2681,1 3228,7 1165.8 396,9 Reaction Forces (kgf) Fig. 12 Reactions in the Bearings
Bearing number 1 2 3 4 5 6 1 66,11 -149,91 107,65 -27.49 5,34 -1.71 2 -149,91 399,58 -370,75 139,50 -27,12 8.69 3 107,65 -370,75 498,71 -328,93 137,31 -44,00 4 -27,49 139,50 -328,93 414,55 -345,48 147,85 S 5,34 -27.12 137.31 -345,48 497,35 -267,40 6 -1,71 8,69 -44,00 147,85 -267.40 156.57
(kgf)/(mm Bearing Vertical Displacement) Fig. 13 Influence Coefficients of the Bearing Reactions
Fig. 14 Elastic Line
Fig. 15 Shear Forces
A
/ \
/
/
i
/
\ / ^ . ^ \..../
A JV
Fig. 16 Bending Moments
Free v i b r a t i o n s calcidation b y the f m i t e element m o d e l indicated the f o l l o w i n g natural frequencies o f the shaft line (same frequency pairs i n orthogonal modes):
1" and 2"-' - Bending at 21.17Hz - Fig. 17 y and é"- - Bending at 24.62Hz - Fig. 18a 5"" and 6"> - Bending at 31.12Hz - Fig. 18b
7* and S"- - Bending at 45.09Hz - Fig. 18c 9"^ - Axial at 47.94Hz - Figure 18d
Def«med(0.G151J: Total Translalion
Fig. 17 1st and 2nd Modes - Lateral Vibration at 21.17Hz
E x p e r i m e n t a l T e c h n i q u e f o r D i a g n o s i n g F r a c t u r e s i n S h a f t L i n e s A p p l i e d t o a R O V S u p p l y V e s s e l Severino Fonseca da Silva Neto, Luiz Antonio Vaz Pinto and José Marcio do Amaral Vasconcellos
18(a) 18(b)
Fig. 18 Lateral Vibration Modes: 3"'& 4"" (a), 5'^& (b), T" & 8" (c); Axial - 9* (d)
N u m e r i c a l results, indicates a b e n d i n g natural frequency o f 21.17Hz. T h i s i n t e r e s t i n g r e s u l t c o u l d e x p l a i n the hypothesis o f resonance c o n d i t i o n close to 2 I H z frequency suggested b y the measured spectra i n the experimental procedure and also the great concentration o f forces close to the box ( O . D Box).
7 Conclusions
The experimental technique f o r diagnosing fractures i n shaft lines applied to a t u g converted to R O V supply vessel was i n t e g r a t e d w i t h n u m e r i c a l techniques a n d its general instrumentation flowchart. The data acquisition system is able to store, manage, select analysis i n f o r m a t i o n , using FFT (Fast Fourier Transform) to make the diagnosis.
The advantage o f this system is the possibility o f accessing i n f o r m a t i o n f r o m b o t h f u l l - s c a l e m e a s u r e m e n t s a n d numerical simulations o f the shaft line, main engine and ship h u l l vibrations.
The j o i n t analysis o f the v i b r a t i o n spectra and numerical models allow the f o l l o w i n g conclusions:
• P e r i o d i c i t y o f fractures and the fact that they occurred after the m o d i f i c a t i o n s made t o the power transmission system (fixed-pitch system to controllable-pitch) points to an inherent cause associated w i t h the new configuration o f the shaft line, factors pile up i n such a way as to lead t o the collapse o f the shaft;
• The modifications undergone by the line shaft include, at the very least, two important alterations: the hollow shaft provides less stiffness relative to the solid section and the existence o f the O.D. Box represents an additional weight ( 1 . 1 5 tons) i n the line shaft;
• It is very likely that the cause of the collapse is not a single one, but rather a combination o f already existing factors that are magnified by the modifications imposed by the new configuration o f the shaft line, being associated w i t h misalignment and resonance i n the 6X frequency.
I n order to m i n i m i z e hmitations i n using regular spectral analysis technique, strictly valid f o r stationary processes emerging from linear systems, in transient phenomena analysis ("cascade diagram"), n u m e r i c a l simulations using direct integration o f the equations are performed before and after acquiring experimental data. A t each appropriate time interval, the displacements, velocities and acceleration o f the discrete model are calculated for load increments, updating the stiffness and mass matrices terms caused by nonlinear dynamic effects
[ Z I E N K I E W I C Z , 1 9 7 9 ] .
8
Future Work
A t t h i s stage, g y r o s c o p i c e f f e c t s [ P R O D O N O F F a n d M I C H A L O P O U L O S , 1 9 7 4 ] o n t u r b o m a c h i n e r y r o t o r d y n a m i c s [ C A S T I L H O , 2 0 0 7 ] are being s t u d i e d a n d techniques based i n superelements a n d c o m p o n e n t m o d e synthesis [ M E I R O V I T C H , 1 9 8 0 ] are being i m p l e m e n t e d to i n c o r p o r a t e , respectively, the n o n l i n e a r effects a n d the i n f l u e n c e o f t h e ship huU o n l i n e shaft coupled t h r o u g h its bearings.
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