kamlesh - ijaetech.com

IJAET International Journal of Application of Engineering and Technology

Vol-4 No.-1

ISSN: 2395-3594

EXPERIMENTAL STUDIES OF MODAL TESTING IN ROTATING MACHINERY

Kamlesh1, Vivek Jha2, Dr. Manoj Chouskey3, Naman Kumar Gandhi4

1,2Student, M.E. (Tribology and maintenance), Shri G.S. Institute of Technology & science Indore (M.P.) 3Professor, Mechanical Engineering Department, Shri G.S. Institute of Technology & science Indore (M.P.)

4Assistant Professor (IIST INDORE)

I. INTRODUCTION

1.1Modal analysis Modal analysis is used to find the dynamic characteristics of structure. These include natural frequency, damping factors and mode shapes. These properties help in understanding the dynamic behaviour of structure. The conditions of resonance can be prevented by the knowledge of natural frequencies. Modal testing is the form of vibration testing of a system and component where modal natural frequencies, masses, damping ratio and mode shape of the object (system) are found out. A modal testing process consists of an acquisition phase and analysis phase. There are several ways to do modal testing but impact hammer and vibration shaker testing are more commonly used. 1.2 Labview Labview (Laboratory Virtual Instrument Engineering Workbench) is a system-design platform and development environment for a visual programming language from National Instruments.The graphical language of it is known as “G”. It is a dataflow programming language. LabVIEW is used for the data acquisition, instrument control and industrial automation. LabVIEW programs are called virtual instruments, or VIs, because their appearance andOperation imitates physical instruments, such as oscilloscopes and multimeters. LabVIEW contains a comprehensive set of tools for acquiring, analyzing, displaying, and storing data. In this software we build a user interface or front panel with controls and indicators.

1.3Frequency Response Function It is mathematically representation of relationship between input and output. We attach accelerometer at one point on system surface and then excite at another point of surface with force gauge instruments Hammer and measuring the excitation force and there response. There are many tools for performing vibration analysis and testing. The frequency response function is a particular tool. Frequency response function (FRF) is a transfer function, expressed in the frequency domain. Frequency response function is complex functions, with imaginary and real components and also be represented in terms of magnitude and phase. A frequency response function is formed by either measured data or analytical functions. A frequency response function expresses the system response to an applied force as a function of frequency. The response may be given in terms of displacement, velocity, or acceleration. Furthermore, the response parameter may appear in the numerator or denominator of the transfer function.

Figure 1 Frequency Response Function

ABSTRACT

Fault diagnosis modal testing studies have been attempted in this work for rotating machinery. Rotating machines, e.g. turbine, motors, pumps etc, may experience many type of faults like unbalance, misalignment, rotor bent, rotor crack etc. In this work A ‘vi’ file have been developed in the NI Labview to experimentally measure the response and force signals and in turn to compute the frequency response function of any system. Many frequency response functions have been measured and the natural frequencies have been found out. Such an analysis may prove helpful in fault diagnosis of geared rotor systems. Keywords: - : Modal Analysis, Gear fault Diagnosis, LabView

415

Kamlesh et al. / International journal of Application of Engineering and TechnologyVol.4 No.-1

In this diagram F{} is the input force as a function of the angular frequency is the transfer function. X{} is the displacement response function. Each function is a complex function, which may also be represented in terms of magnitude and phase. Each function is thus a spectral function. There are numerous types of spectral functions. For simplicity, consider each to be a Fourier transform. The relationship between above diagram can be represented by the following equations

X () = H() .F() (1)

H () = X()/F() (2)

Similar transfer functions can be developed for the velocity and acceleration responses. 1.4Natural Frequency Bridges, aircraft wings, machine tools, and all other physical structure or system has natural frequencies. A natural frequency is the frequency at which the structure or system would oscillate if it is disturbed from its rest position and then allowed freely vibrates. All structure or systems have at least one natural frequency. Nearly every structure or system has multiple natural frequencies.

II. EXPERIMENTAL WORK & SETUP

In this Experimental investigation of natural frequencies of a geared rotor system. This has been accomplished by measuring the frequency response functions of the system. Fundamentally a frequency response function (FRF) is a mathematical representation of the relationship between the input and the output of a system. Basically, it is defined as the ratio of the output of the system in the frequency domain to the input of the system in the frequency domain.

Mathematically:

Y (f )H (f )

X (f ) (.3)

FRF is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is the transfer function with real and imaginary components and can also be represented in terms of magnitude and phase.

III. EXPERIMENT PROCEDURE

The frequency response of a system can be measured by:

1. Applying an impulse to the system and measuring its response.

2. Sweeping a constant-amplitude pure tone through the bandwidth of interest and measuring the output level and phase shift relative to the input.

3. Applying a signal with a wide frequency spectrum (for example digitally-generated maximum length sequence noise, or analog filtered white noise equivalent, like pink noise), and calculating the impulse response by deconvolution of this input signal and the output signal of the system.

For the estimation of the FRF while performing modal analysis, it is required to attach an accelerometer at particular point and excite the structure at another point with force gauge instrumented hammer. Further by measuring the excitation force (stimulus signal) and the response of the accelerometer (response signal), FRF can be obtained.

Figure 2 experimental Setup

3.1 Acquisition of the experimental data using LabVIEW software

3.1.1 Block Diagram Block diagram contains the graphical source code of a LabVIEW program. The block diagram is shown in Figure in which the virtual instrument (VI) and structure are used.

Figure 3 Block Diagram 3.1.2Procedure –

1. Firstly create VIs- right click- Express – Input - DAQ assistant and then double click on assistant

416


and put sensitivity of accelerometer and impact hammer then click OK.

2. Again in express – signal manipulation – select signal. Two signals are acceleration and force.

3. Again right click go to the sound and vibration – FFT- FRF and double click on FRF are various parameters i.e. magnitude, phase, real and imaginary coherence.

4. DAQ assistant and FRF to right click and create graph indicator.

1) Front panel

Front panel is the user-interface which provides us to visualize the signals from the sensors. The waveform graphs are used for the signal visualization. Each waveform graph shown are the indicators in the block diagram. The front panel is shown in Figure.

Figure 4III Front panel

3.2 Measurement Point The two main factors need to be taken into consideration while selecting measurement points: (i) the number of measurement points and (ii) the location of each measurement point. The minimum number of points are chosen such a way that the result of FRF can be obtained accurately. As the experiment is performed on the geared rotor system the point are taken only along the length and as our purpose is only to find the FRF the number of points chosen is sufficient.

Figure 5 Measurement point on geared rotor system

IV. RESULTS AND DISCUSSION

4.1 Frequency response functions for response measured at point 5

Frequency response This signal is obtained from the mathematical relation between the stimulus and response signal.

Measured FRFs are shown for response measured at point 5 and force applied at points 1, 2, 3, 4, 6, 7 and 8. These FRFs are shown in Figure.

Measured FRFs are shown for response measured at point 5 and force applied at points 1, 2, 3, 4, 6, 7 and 8. Overlay of frequency response functions is shown in Figure 5. The noted natural frequencies from the FRFs are shown in Table 1

Figure 6 Overlay of frequency response functions

4.2 Table for Natural Frequency

Table 1 Natural Frequency of System

4.3 Frequency response functions for

response measured at point 7 Overlay of frequency response functions is shown in Figure 7. The noted natural frequencies from the FRFs are shown in Table 2.

Modes Natural Frequencies(Hz)

First 35

Second 121

Third 215

Fourth 382

Fifth 434

417


Figure 7Overlay of frequency response functions

Table 2 Natural Frequency of System

V. CONCLUSION

A ‘vi’ file have been developed in the NI Labview to experimentally measure the response and force signals and in turn to compute the frequency response function of any system.

The developed ‘vi’ file has been used to measure the frequency response function of geared rotor system.

Many frequency response functions have been measured and the natural frequencies have been found out. Such an analysis may prove helpful in fault diagnosis of geared rotor systems.

Experimental modal analysis of gear rotor system can be carried out to find out its mode shapes.Measured natural frequencies can be validated using numerical methods like finite element method.Time frequency analysis and order

analysis can be performed in fault diagnosis of rotating machinery.

REFERENCES

1. Ambekar, A. G. (2010). “Mechanical Vibrations and Noise Engineering”. New Delhi, PHI Learning Private Limited.

2. Ewins, D. J. (2000a). "Basics and State-of-the-Art of Modal Testing." Sadhana25(3): 207-220.

3. Ewins, D. J. (2000b). “Modal Testing: Theory, Practice and Application”, Research Studies Press, Baldock, Hertfordshire, England.

4. Irvine T. (August 2000), “The Steady-State Response of a Single-Degree-of-Freedom System Subjected to a HarmonicForce”, Vibrationdata.com Publications.

5. Arora V. (2014). "Structural Damping Identification Method using Normal FRFs." International Journal of Solids and Structures51(1): 133-143.

6. Ashory, M., et al. (1998). "Generation of the Whole FRF Matrix from Measurements on One Column." SPIE proceedings series: 800-814

7. Verboven P., Dr.Guillaume P., Prof. Dr.Van M. (May 2002), “Frequency- Domain System Identification for Modal Analysis”. VRIJE University, Brussel, Belgium.

8. Kumamoto et al (2004) “A Study on Relationship between Pad Restraint Condition and Brake Squeal Generation”, SAE technical paper 2004-01-2801(p.1-7).

9. Shah H. (November 2012) “Online Condition Monitoring of Spur Gear” The International Journal of Condition Monitoring Vol. 4.

10. Labview Sound and Vibration Kit Details, www.ni.com

11. Choi and Han (2009) “Active Vibration Control of A Flexible Beam using a Non-Collocated Acceleration Sensor and Piezoelectric Patch Actuator”, Journal of Sound and Vibration 438–455.

Modes Natural Frequencies(Hz)

First 35

Second 121

Third 215

Fourth 382

Fifth 434

417

418

Documents

kamlesh - ijaetech.com