Chapter- 8 MODAL ANALYSIS AND CONDITION MONITORING Syllabus: Signal analysis, dynamic testing of machines and structures, Experimental modal analysis, Machine condition monitoring and diagnosis. Dynamic testing of machine structure involves the finding the deformation of machines at a critical frequency. Dynamic testing is a valuable complement to dynamic analysis. It can be done using the following: I method: Forced dynamic deflection shape measured under steady state frequency of system. It involves an accelerometer is mounted at some point on the machine as a reference and another moving accelerometer is placed at several other points and in different directions. The magnitude and phase differences between the moving and stationary ( reference) accelerometer at all points under steady state operation of the system are measured. By plotting these we can find the deflection of parts of machine move relative to another. Using operational deflection shape measurements. The deflection shape measured is valid only for the force/frequency associated with the operating conditions.
II method: Using modal testing Any dynamic response of a machine can be obtained as a combination of its modes a knowledge of mode shapes, modal frequencies and modal damping ratios constitute a complete dynamic description of the machine. EXPERIMENTAL MODAL ANALYSIS: Basic idea 1. When a structure machine or any system is excited its response exhibits a sharp peak at resonance. 2. The phase of the response changes by 180° as the forcing frequency crosses the natural frequency of the structure or machine. The necessary equipment 1. An exciter or source of vibration to apply a known input force to structure.
2. A transducer to convert the physical motion of the structure or machine into electrical signal. It translates changes in mechanical quantities (such as displacement, velocity, acceleration or force) into electrical signals (such as voltage or current). Mr. Venkatesh B K
Dept. of Mechanical Engg. NCET, Bangalore Page 1
3. A signal conditioning amplifier to make the transducer characteristic compatible with the input electronics. 4. An analyzer to perform the tasks of signal using suitable software. Exciter The exciter may be an electromagnetic shaker or an impact hammer , the electromagnetic shaker can provide large impact forces so that the response can be measured easily. The excitation signal is usually of a swept sinusoidal or random type signal. Usually shaker is attached to the structure or machine through the short thin rod called a stringer to isolate the shaker ,reduce the added man and apply the force to structure or machine. Transducer Among the transducer the piezo electric transducer are most popular. A piezo electric transducer can be designed to produce signals proportional to either force or acceleration. In acceleration, the piezo electric material acts as a stiff spring that causes the transducer to have a resonant or natural frequency. Signal conditioner Since the output impedance of transducer is not suitable for direct i/p to the signal analysis equipment, signal conditioner in the form of charge or voltage amplifiers are used to match and amplify. Analyzer The response signal, after conditioning is sent to analyzer for signal processing. A commonly used analyzer is called a fast Fourier transform analyzer. Such as analyzer receiver analog voltage signals form a signal conditioning amplifier, filter and digitizer for computations. It computes the discrete frequency spectra of individual signals as well as cross-spectra between the input and the different output signals. The analyzed signals can be used to find the natural Mr. Venkatesh B K
frequencies damping ratio’s and mode shapes either in numerical or graphical form. Digital signal processing The analyzer converts the analog time domain signals X(t)in to digital frequencydomain data using Fourier series relations to facilate digital computation. Thus the analyzer accepts the analog output signals of accelometers or force transducers, X(t) and computes the spectral co-efficient of signals a0,an and bn in frequency domain. The process of converting analog signals in to digitals is indicated in the Figure.
X(t) – analog signal, X(ti)- represents corresponding digital record with ti indicates its discrete value of time. If N no of X(t) is collected as discrete value of time ti the data. X1 (ti) X2 (ti) –XN (ti). Xj=X(tj) = ) ao = bi= The equation can be expressed in matrix form,
Computed using FFT by the analyzer. Dept. of Mechanical Engg. NCET, Bangalore Page 2
Analysis of random signals:The out and input data measured by the transducers usually contains some random component or noise that make it difficult to analyses. In a deterministic manner in some case random excitation is used is vibration testing. Thus random signal analysis becomes necessarily in vibration testing. If X(t) is a random signal. The average or mean denoted as
Corresponding to any random signal y(t)and a new variable x(t) as x(t)= y(t)- y(t) so that mean value of x(t)is zero. Hence without loss generating we can assume that X(t) to have a zero mean and define the mean
S(w) is power spectral density of random signal x(t) denoted as s(w), gives the measure of speed with which the signal change is frequency domains.
Co-herence function; A function known as B is defined as a measure of noise presents in signal.
Determination of modal data from observed peaks:The frequency response function H(iw) can be used to find the natural frequency, damping ratio, and mode shapes, corresponding to all resonant peaks. Let the graph of frequency – function as shown in below.
X(t ) t
square value or variance of X(t).
The root mean square velocity (rms) Xrms= The auto co relation function of random signal X(t) denoted as R(t). It gives the measure of the speed with which the changes in the time domains
The response output from the system being tested can be modeled as four degree of freedom if the resonance frequency closely spaced in graph H(iw). Here frequencies ranges are proportioned these are considered as the frequency response function of a single degree of freedom. This mode represents a resonance point corresponding to a phase angle to be 900 at each of the peaks. The damping ratio is given by. and
S
are known as half
power points
Mr. Venkatesh B K
Dept. of Mechanical Engg. NCET, Bangalore Page 3
1. Since the damping is small it can be considered approximately equal to undammed natural frequency of system. 2. Determination of model data from nyquist plot. 3. Determination of modal data from bode plot. 4. Measurement of mode shapes. Machine diagnosis
condition
monitoring
and
3) Condition based maintenance: The fixed- interval over hours are replaced by fixed –interval measurements that permit the observation of changes in the running condition of the machine regularly. These vibrations are measured regularly. If vibration levels are unacceptable the machine should be serviced. This is also called predictive maintenance. In this method the maintance casts are greedily reduced due to fewer catastrophic failures. Machine techniques:
Failur e
monitoring
Machine condition Monitoring
Vibration
1) Break down maintenance: The machine is allowed to fail, at which time the failed, machine is replaced by new one. This strategy can be used if machine is in expressive. 2) Preventive maintenance: Maintenance is performed at fixed intervals such as very 3000 operating hours or once year. In intervals are determined statistically from past experience. This method is found to be uneconomical.
Wear Debris
1) Break down maintenance. 2) Preventive maintenance. 3) Condition based maintenance.
Temp
Three types of maintenance schemes can be used
Operation Variables
The life of machine follow classical bath tub curve shown in above figure of a machine is usually characterized by increase in vibration. The vibration level decreases during initial condition. They remains constant in normal condition and increase rapidly due to serve wear out.
Visusa
Machine maintenance technique
Auras
time
Mr. Venkatesh B K
condition
Several methods can be used to monitor the condition of a machine. Machine condition monitoring Auras & visual: These are basics forms of monitoring technique in which skilled technician, having an intimate knowledge of machine can identify the faults by listen its sounds; visually observing large amplitude by using stroboscope, microphone. Ope ration variables: It’s a duty cycle monitoring performance of m/c is observed with regard to its intended duty any deviation from intended duty denotes malfunction of m/c. Temp involves measuring of surface temp of machine devices used are optical pyrometer, thermo couple, thermo graphy. Wear debris: Wear debris is generated as relative moving surfaces of load-bearing m/c elements. The wear particles can be found in
Dept. of Mechanical Engg. NCET, Bangalore Page 4
lubricating oils or grease can be used to arren the extent of damage. Machine vibration mounting technique 1. Time domain technique a) Wave form b) Shaft orbits c) Statistical analysis 2. Frequency domain technique 3. Quefrency domain Time domain analysis: Time wave form: time domain analysis uses the time history signal. The signal is stored in an oscilloscope or real time analyses are any non steady impulses are noted. Discrete damage such as broken teeth is gears and crack in inner or outer races are shown by wave form of gear box.
density of a signal can be defined on the probality of finding its instantaneous amplitude within a certain range. The good conditioned components will have a bell shaped probability density curve similar to normal distribution. Moments of probability density curve can be used for the machine condition monitoring. These are similar in mechanical moments about the centroidal axis of area. Frequency domain analysis: Frequency spectrum: It is a plot of the amplitude versus frequency. It can be derived by using digital fast Fourier analysis of time waveform. The vibration response of machine is governed not only by its assembly, mounting and installation. As long as the excitation force remains constant the measured vibration level of the machine also remains constant. By comparing the frequency spectrum of machine in good condition and as in faulty condition, the nature and location of the fault can be detected. Quefrency domain analysis: Quefrency serve as the abscissa for a parameter known
This indication that acceleration wave form pulses occur periodically with period of 20 millisecs. This origin of signals can be attributed to broken gear tooth. Shaft orbit : Certain patterns called orbit can be obtained by displacing time waveform obtained from two transducer whose outputs are shifted by 90o. Any change in pattern of these figure or orbit can be used to identify faculty such as misalignment in shaft, unbalance in shaft, shaft rub, and wear in journal bearings. Statistical methods: Probability density curve: All vibration signals will have a characteristic shape for its probability density curve. The probability Mr. Venkatesh B K
as cepstrum similar to frequency that serves as the abscissa for the parameter spectrum. Cepsturn is useful in machine condition monitoring and diagnosis since it can detect any periodity to the spectrum caused by the failure of components such as blade in turbine and gear tools in a gear box. ***BEST OF LUCK*** Dept. of Mechanical Engg. NCET, Bangalore Page 5
