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VIBRATION ANALYSIS NEED 1. Increase in demands of higher pdty & economical design lead to higher speeds of machinery and efficient use of light wt mtls. It make the occurrence of resonant condition during the operation of m/c. Hence, measurement of vibration charact. of m/c becomes essential to ensure safety margin. Other vibration charact. Any shift indicate failure/ need for maint. of m/c. 2. Measurement of nat. freq. of m/c is useful in selecting the operational speeds of m/c. 3. Theoretically computed vib. charact. May be different from actual values due to assumptions
4. Measu. of freq. of vib.and forces is necessary in the design vib isolation systems 5. To det. the survivability of m/c. If the m/c performs its task under testing conditions, it is expected to survive in the specified condition 6. Continuous system –approx. to muti dof. If the measured freq. & mode shapes are comparable to the computed nat freq. and mode shape, then only the approx is valid 7. Measur. of I/P and resulting vib. charact. helps in identifying the system in terms of k, m 8. Information about ground vib. due to earthquake, ocean waves and road surface roughness is important in design og m/c, structures, and vehicle suspension systems.
VIBR. MEASUREMENT SCHEME • Considerations for selecting instrument
Vibrating m/c
Transducer
Motion of vib body into elec. signal
Signal conver. instrument
Display unit
Data analysis
Amplify elec. signal
– Range of frequencies – Size of m/c – Operating conditions of m/c, structure, equipments – Type of data processing used (graphical display/recording/stroing)
Presentation for visual inspection and stored in computer To det. Vib charact. Of m/c
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TRANSDUCERS • Device that transforms physical variables into electrical signals • Types
VARIABLE RESISTANCE TRANSDUCER
values of equivalent
– Variable resistance transducer – Piezoelectric transducers – Linear Variable Differential transformer transducer
• In this m/cal motion produces change in electrical resistance in the o/p volatge • It consists of fine wire(Cu-Ni alloy known as advance) whose resistance changes during vib. • Fine wire is sandwiched b/w 2 thin paper sheet. • Bonded to surface where the strain is to be measured. • If surface undergoes a normal strain(ε), the strain gage also undergoes same strain and the change in resistance is
R / R rL K 1 2 1 2 L / L r L
• • • • • • • •
K- Gage factor of the wire R- Initial resistance ΔR- Change in resistance L- Initial length of the wire ΔL- Change in length of the wire ν – poisson’s ratio of the wire r- resistivity of the wire Δr- Change in resistivity of the wire ≈0 for Advance
L R L RK
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• The strain gage is mounted on an elastic element of a spring mass system • Strain is proportional to deflection of mass x(t) and indicated by strain gage
• The change in resistance ΔR can be measured by Wheatstone bridge • In the Wheatstone bridge voltage V is applied and the resulting voltage E is given by
RR R R E V R R R R 1
1
3
2
2
3
4
4
Initially R1R3=R2R4 Strain gauge as vibration pick up Wheatstone bridge
• When resistance changes, the change in output voltage R R R R E Vr R R R R 1
2
3
PIEZOELECTRIC TRANSDUCERS
4
0
1
r 0
2
3
4
RR RR R R R R 1
1
3
4
2
1
1
2
3
4
If the leads are connected to ‘a’ and ‘b’, R1=Rg, ΔR1= ΔRg, ΔR2= ΔR3 =ΔR4= 0 then ΔRg/Rg= ΔE/Vro=εK; ΔE=KVroε Rg-Initial resistance of the gage O/P voltage is proportional to strain
PIEZOELECTRIC ACCELEROMETER
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• Quartz, Tourmaline, Lithium sulfate generates electrical energy when subjected to deformation or m/cal stress. • Elect. charge disappears when m/cal load is removed • Such mtls -Piezo electric mtls, -Piezo electric transducers,Piezo electric effect • Energy generated Qx=kFx=kApx • k-Piezoelectric constant(2.25X10-12 -Quartz)), A-Area on which the force applied, px-Pressure • O/p voltage of the crystal E=vtpx • V-voltage sensitivity(0.055 voltmeter-Quartz)
LINEAR VARIABLE DIFFERENTIAL TRANSFORMER TRANSDUCER
• One py coil and two 2ndary coil • Magnet core move inside in an axial direction • When a.c i/p is given to py coil, the o/p is diff. of voltages induced in 2ndary coil • o/p depends magnetic coupling b/w coil & core • Core is in middle-o/p is zero • On either side-there is o/p • Range of displacement – 0.0002 cm -40 cm
SEISMIC INSTRUMENT (VIBROMETER AND ACCELEROMETER)
Displacement transducer
Seismic mass (m)
Housing x
Spring Y=Yosinωt
O/p voltage
Linearity of o/p with disp.
WORKPIECE
Displ. Of core
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• An instrument which has the functional form of mass connected thro’ damper and spring arrangement to housing frame • Frame is connected to sources of vibr. whose charact to be measured • Mass tends to remain fixed in its position so that vibr. motion is registered as a relative displ. b/w mass & frame & sensed by transducer • Seismic instrument may be used for either displ. or acceleration measurements by proper selection of mass, spring and damper • Large mass & soft spring-Vibr. Displ. Measure • Small mass and stiff spring-Acceleration
• • • •
• • • •
Transducer with other device to measure vibr. Commonly used –Seismic instrument Consists mass-spring-damper on vibrating body Then the vibratory motion is measured by finding the displ. of the mass relative to the base on which it is mounted Displ. of nass relative to cage z=x-y x-displ. of suspended mass,y-displ. of cage Vibrating body executes SHM y(t) = Ysinωt Eqn of motion mx c ( x y ) k ( x y ) 0
VIBRATION PICKUPS
mz cz kz mY sin t Soln
z(t)=ZSin(ωt-φ)
Z
Y 2 ( k m 2 )2 c 2 2
c tan 1 k m 2
mz cz kz my
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FREQUENCY MEASURING INSTRUMENTS FULLARTON TACHOMETER(SINGLE REED INSTRUMENT)
FRAHM TACHOMETER (MULTI REED INSTRUMENT)
• Consists variable length cantilever strip with mass at one end and other end is clamped. • Free length can be changed by screw • Since, each length have different frequency, reed is marked with frequency • Clamped end is pressed against vibrating body and screw is adjusted until the free end shows largest amplitude of vibration. • When excitation frequency = nat frequency, it can be read from the strip
• Consists no of reeds with mass at ends • Each reed has different frequency and marked on it • Mounted on vibrating body and the reed vibrates with frequency of vib. Body has largest amplitude • The frequency of reed = unknown frequency
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STROBOSCOPE
• Produces light pulses intermittently • The frequency at which the pulses are produced can be altered and read from the instrument • When the frequency of vibrating object is equal to the frequency of pulsating light, the point on vibrating body is stationary • Advantages – No contact with vib. Body – Measure lowest freq.
VIBRATION EXCITER
MECHANICAL EXCITER
• M/C which produces the m/cal motion to which the test object is subjected • Used in determination of dynamic charact. of m/c and structure and fatigue testing of matls. • The exciter may be designed to produce a given range of harmonic or time dependent excitation force or displacement through a a given range of frequencies • Classified into mechanical, hydraulic, electrodynamics
VIBRATION BY INERTIA FORCE
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MECHANICAL EXCITER Scotch yoke m/sm can be used to produce harmonic vibrations. The crank can be drive by const or variable speed motor • When structure is to be vibrated the harmonic force can be applied as an inertia force or as an elastic spring force • These vibrators are used for frequencies <30 HZ and load < 700 N VIBRATION BY AN ELASTIC SPRING FORCE
• The unbalance created by two masses rotating at the same speed in opposite direction can be used as a m/cal exciter • It can be used for 250 and 25000 N. • If 2 masses of magnitude ‘m’ each, rotate at an angular velocity ω at a radius R, the vertical force F(t) =2mRω2cos ωt • Limited frequency range • No control over the force
VIBRATION EXCITATION DUE TO UNBALANCED FORCE
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HYDRAULIC EXCITER
ELECTRODYNAMICE EXCITER
• Uses piston-cylinder arrangement and the movement is controlled by fluid pressure • Since the fluid pr can be controlled, wide range of force can be obtained • Can generate low frequencies • Used for testing civil engg structures
RESONBANCE CHARATERISTICS OF ELECTRODYNAMIC SHAKERR
• Called as electromagnetic exciter • When current passes thro’ a coil passed placed in a magnetic field, force ‘F’ proportional to current ‘I’ and magnetic flux density ‘D’ is produced which the accelerates the object on the shaker F=DIL (L-length of coil) • Magnitude of accel. depends max. current & mass of object & moving element of the shaker • If a.c current is used, forces varies harmonically • If d.c current is used, const.forces is generated • Exciter has 2 freq. one corresp. to nat freq of flexible support an other corresp. To nat. freq. of moving element • Operating freq of exciter lies b/w these two freq. • Used to generate forces upto 30,000N, displacement – 25 mm, Freq -5 Hz to 20 KHz
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SIGNAL ANALYSIS •To det the freq response of system under known excitation •Signal analysis is done by -Spectrum analyzer -Octave and 1/3rd octave filters -Bandpass filter (for sequential analysis) -Real time analysis (for transient signal analysis )
SPECTRUM ANALYZERS • Device that analyzes a signal in the frequency domain by separating the energy of the signal into various frequency bands • Separation is done by filters • In recent days digital analyzers are popular • Used for machine condition monitoring
OCTAVE &1/3RD OCATVE FILTER •Vibratory signal of a m/c under steady state condition in time domain is called as signature •Used to obtain the vibrat. levels for all discrete freq. components in m/c sign. over wide range •Fig shows response charact of octave filter •Desired no of filters-to cover given range of freq. •Example: Octave filter with freq. 31.5, 63, 125, 250 & 500Hz- to obtain vibrat. levels over 5bands. •To improve analysis 1/3rd octave-with freq. 20, 25, 31.5,40,50,63,80,100,125,160,200,250Hz etc.
31.5 63
125 250 500
RESPONSE CHARACT. OF ACTAVE BAND FILTER
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BAND PASS FILTER (TUNABLE FILTER)
RESPONSE OF A FILTER
REAL TIME ANALYSIS • If vibr. signal is transient RTA is useful •O/P is presented in TV type of tube to facilitate to observe the spectrum continuously and capture whichever portion of the signal is desired and recorded. Magnetic tape is used for recording so that the signature can be stored for playback
• Permits the passage of frequency components of a signal over a frequency band and rejects all other freq. components of the signal • Graph shows the response charact. of a filter whose lower and upper cut off freq are fl and f u. • Practical filter will have a response charact. deviating from ideal rectangle • f c-Centre frequency • In Constant percent bandwidth filter,band width (f u-f l)/f c is constant • In Constant bandwidth filter,(f u-f l) is independent of f c
VIBRATION TESTS • To know system charact. ie nat freq, corresp. mode shapes, & nature and amt of damping • 1) Free vib. Test – In this, system is displaced from its mean position and released. The resulting free vibrations are recorded in the oscilloscope from which information regarding nat freq. & damping can be obtained
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2) Forced vibr. Test – Produces accurate &complete information – System is subjected to unidirectional harmonic force at a desired freq. using suitable shaker (eg. Electrodynamic shaker) and response is recorded by accelerometer – Excitation freq is varied at regular intervals and response is plotted as a fn of freq. and system performance is studied – Servo controlled shaking system can be used to conduct this test automatically and reduce the testing time. Such test is sweep test. Excitation freq is varied continuously and response is plotted as a fn of freq. and system performance is studied
• For rotating machinery, rundown test can be conducted • Initially m/c is brought to more than service speed. Then power is cut off and allowed to coast down to zero speed due to damping in the system. Damping is small and coating period is large enough to allow the amplitudes to build up (resonance effect) as the m/c passes through its critical speeds.
Examples Vibration tests OSCILLOSCOPE
Fig. 9.25 •Fig. shows a tapered beam model of a turbine blade. To det. Freq and mode, it is mounted on test rig. Blade is vibrated by electrodynamic shaker. Vibrations are measured by accelerometer mounted on the beam and displayed in oscilloscope. •Sweep test is conducted first with centre point excitation (at A) to obtain bending modes and then with end excitation (at B) to obtain torsion modes
OSCILLATOR ACCELEEROMETER
POWER AMPLIFIER
PREAMPLIFIER
EXCITER
Instrument for deter. of nat. freq of turbine blade
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RESONANT FREQ OBTAINED FROM CENTRE PT EXCITATION
SNO 1 2
RESONANT FREQ.(Hz) 482 1960
3
REMARKS
RESONANT FREQ OBTAINED FROM END PT EXCITATION
SNO
Nat. mode,1st bending(1B) Coupled mode(2B+1T)
1 2
RESONANT FREQ.(Hz) 482 1910
2580
Nat. mode, 2nd bending(2B)
3
2340
Coupled mode(2B+1T)
4
4800
Nat. mode, 3rd bending(3B)
4
2510
Nat. mode, 2nd bending(2B)
5
5880
Weak resonance
5
4910
Nat. mode, 3rd bending(3B)
6
8820
Patterns not traceable
6
5850
Nat. mode,2nd trosion(2T)
7
8800
Weak resonance, nodal Patterns not traceable
• Blade is excited at predet resonant freq and nodal lines are determined. Blade C N
D
Nodal line
At C Ampli. of measured signal At N
At D
REMARKS Nat. mode,1st bending(1B) Nat. mode,1st trosion(1T)
• Harmonic signal from the oscillator is fed to vertical plates of oscilloscope • O/P from accelerometer probe is fed to hori plates. Since both signals are of same freq ellipse is observed. • consider C and Don 2 sides of a nodal pt N. • signals at C&D are in phase opposition • Pt A is nodal pt in torsional vib and hence torsional modes are suppressed • With end excitation, both bending and torsional modes are excited, the bending modes coupled with torsional motion.Thus the first 3 bending nat freq are 482, 2850 and 4800 • And first 2 torsional nat freq -1910 and 5850Hz.
Amplitude of ref. signal DET OF NODAL PATTERNS
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