random vibration analysis of aerospace …ipasj.org/iijme/volume3issue2/iijme-2015-01-24-1.pdf ·...

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IPASJ International Journal of Mechanical Engineering (IIJME) Web Site: http://www.ipasj.org/IIJME/IIJME.htm A Publisher for Research Motivation........ Email: [email protected] Volume 3, Issue 2, February 2015 ISSN 2321-6441 Volume 3, Issue 2, February 2015 Page 1 ABSTRACT An Aerospace vehicle is subjected to different loading conditions during its flight. Some of them are Aerodynamic, Thermal and Inertial. Vibration is a penalty that is always present throughout the vehicle flight, resulting in disturbance in flight mission. The sources of vibration are Aerodynamics, Propulsion and Acoustics. These vibrations are random in nature. The vehicle carries Mechanical and Electrical systems for its Controls, Guidance, Propulsion and Payload during its flight, to its destination. These Mechanical and Electrical systems are directly exposed to these loads or vibrations. During the design and development stage of Aerospace vehicle the systems are qualified for these loads. The Qualification of Mechanical and Electrical systems include experiments in which huge setup is required that incurs lot of expenditure. In the present work, Random vibration analysis of an equipped section of airframe is carried out and the results are validated by experiment. By performing random vibration analysis, the project cost can be reduced, the shelf life of the systems carried by the flight vehicle can be increased and if any design modifications were required in the configuration, it can be done at minimum cost and less human effort. The study starts with introduction of the problem, Aerospace vehicle, Analysis followed by Literature survey, procedure for Random Vibration Analysis, Experiment setup for random vibration test, and Results and Conclusions. Keywords: Random vibration, Aerospace vehicle, Structure, PSD, Analysis, etc. 1. INTRODUCTION An Aerospace vehicle will have Propulsion system, Structures, Payload, controls, guidance. Number of critical components that includes both Mechanical and Electrical participate in the flight mission. During the mission, the Propulsion system, acoustic and Aerodynamics of the vehicle cause undesired vibration. These vibrations are random in nature. For the ease of integration and testing of the vehicle, the airframe structure of complete Aerospace vehicle is split into number of sections. In order to qualify these sections and its critical systems for the mission they are subjected to random vibration test. In the development stage these kind of test are iterative in nature to qualify. Hence finite element method is used to simulate the flight and its vibration conditions to reduce the cost. In this work focus is on simulating the electronic section of a typical Aerospace vehicle and its vibration condition. Here solid modeling of airframe section, electrical sub systems, is carried out. The result of analysis is validated with the experiment carried out on flight of the electric sections with same parameters. The subsequent chapters will explain this procedure of modeling, analysis, experiment and its data, results. 2. Motivation The Aerospace vehicle during its flight is subjected to vibrations that are random in nature. These vibrations are predominant during the frequency bandwidth of 20 to 2000Hz. The sources of these vibrations are Aerodynamics, Propulsion and Acoustics of vehicle. In an Aerospace industry, Performing tests and experiments on the vehicle and its airframe sections are quite expensive and time consuming. Computer generated models are usually developed by simulating the weight and Centre of gravity of the actual flight hardware so that they are validated with them for different studies like modal test, random vibration test. The advantages involved in using computer generated model are; a) Economy b) saving experimental set up time c) No separate set up for performing tests d) the durability of critical systems can be increased e) The computer generated models can be shared easily and comfortably by different committees for reviewing the test and test unit RANDOM VIBRATION ANALYSIS OF AEROSPACE VEHICLE STRUCTURE G. Durga Prasad 1 , Dr. K. Lalit Narayan 2 , K. Manoj 3 , B.V.Subramanyam 4 1 M.E. Machine Design, Sir C.R.Reddy college of Engineering, Eluru, 2 Professor, Sir C.R.Reddy college of Engineering, Eluru, 3 Scientist ‘D’, R.C.I, DRDO, Hyderabad 4 Assistant Professor Sir C.R.Reddy college of Engineering, Eluru

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Page 1: RANDOM VIBRATION ANALYSIS OF AEROSPACE …ipasj.org/IIJME/Volume3Issue2/IIJME-2015-01-24-1.pdf · Random vibration analysis of an equipped section of ... “Introduction to Random

IPASJ International Journal of Mechanical Engineering (IIJME) Web Site: http://www.ipasj.org/IIJME/IIJME.htm

A Publisher for Research Motivation........ Email: [email protected] Volume 3, Issue 2, February 2015 ISSN 2321-6441

Volume 3, Issue 2, February 2015 Page 1

ABSTRACT An Aerospace vehicle is subjected to different loading conditions during its flight. Some of them are Aerodynamic, Thermal and Inertial. Vibration is a penalty that is always present throughout the vehicle flight, resulting in disturbance in flight mission. The sources of vibration are Aerodynamics, Propulsion and Acoustics. These vibrations are random in nature. The vehicle carries Mechanical and Electrical systems for its Controls, Guidance, Propulsion and Payload during its flight, to its destination. These Mechanical and Electrical systems are directly exposed to these loads or vibrations. During the design and development stage of Aerospace vehicle the systems are qualified for these loads. The Qualification of Mechanical and Electrical systems include experiments in which huge setup is required that incurs lot of expenditure. In the present work, Random vibration analysis of an equipped section of airframe is carried out and the results are validated by experiment. By performing random vibration analysis, the project cost can be reduced, the shelf life of the systems carried by the flight vehicle can be increased and if any design modifications were required in the configuration, it can be done at minimum cost and less human effort. The study starts with introduction of the problem, Aerospace vehicle, Analysis followed by Literature survey, procedure for Random Vibration Analysis, Experiment setup for random vibration test, and Results and Conclusions. Keywords: Random vibration, Aerospace vehicle, Structure, PSD, Analysis, etc.

1. INTRODUCTION An Aerospace vehicle will have Propulsion system, Structures, Payload, controls, guidance. Number of critical components that includes both Mechanical and Electrical participate in the flight mission. During the mission, the Propulsion system, acoustic and Aerodynamics of the vehicle cause undesired vibration. These vibrations are random in nature. For the ease of integration and testing of the vehicle, the airframe structure of complete Aerospace vehicle is split into number of sections. In order to qualify these sections and its critical systems for the mission they are subjected to random vibration test. In the development stage these kind of test are iterative in nature to qualify. Hence finite element method is used to simulate the flight and its vibration conditions to reduce the cost. In this work focus is on simulating the electronic section of a typical Aerospace vehicle and its vibration condition. Here solid modeling of airframe section, electrical sub systems, is carried out. The result of analysis is validated with the experiment carried out on flight of the electric sections with same parameters. The subsequent chapters will explain this procedure of modeling, analysis, experiment and its data, results. 2. Motivation The Aerospace vehicle during its flight is subjected to vibrations that are random in nature. These vibrations are predominant during the frequency bandwidth of 20 to 2000Hz. The sources of these vibrations are Aerodynamics, Propulsion and Acoustics of vehicle. In an Aerospace industry, Performing tests and experiments on the vehicle and its airframe sections are quite expensive and time consuming. Computer generated models are usually developed by simulating the weight and Centre of gravity of the actual flight hardware so that they are validated with them for different studies like modal test, random vibration test. The advantages involved in using computer generated model are;

a) Economy b) saving experimental set up time c) No separate set up for performing tests d) the durability of critical systems can be increased e) The computer generated models can be shared easily and comfortably by different committees for reviewing the test

and test unit

RANDOM VIBRATION ANALYSIS OF AEROSPACE VEHICLE STRUCTURE

G. Durga Prasad1, Dr. K. Lalit Narayan2, K. Manoj3, B.V.Subramanyam4

1M.E. Machine Design, Sir C.R.Reddy college of Engineering, Eluru,

2Professor, Sir C.R.Reddy college of Engineering, Eluru,

3Scientist ‘D’, R.C.I, DRDO, Hyderabad

4Assistant Professor Sir C.R.Reddy college of Engineering, Eluru

Page 2: RANDOM VIBRATION ANALYSIS OF AEROSPACE …ipasj.org/IIJME/Volume3Issue2/IIJME-2015-01-24-1.pdf · Random vibration analysis of an equipped section of ... “Introduction to Random

IPASJ International Journal of Mechanical Engineering (IIJME) Web Site: http://www.ipasj.org/IIJME/IIJME.htm

A Publisher for Research Motivation........ Email: [email protected] Volume 3, Issue 2, February 2015 ISSN 2321-6441

Volume 3, Issue 2, February 2015 Page 2

f) Easy to modify the model than the flight hardware in accordance to the comments or observation given by different committees during review.

These advantages lead the designer mainly towards saving the Project budget and product development time that are very important for withstanding the competition in the market. So In the present work, a computer generated model of an airframe section is developed, analyzed for an input of random vibration and analyzed the output at specified locations. In this project we perform random vibration analysis of equipped airframe section among is validated with experimental results.

3. Model analysis

In modal analysis we chose the 20 mode shapes and also 20 mode expansions and constrain the model at rear bulk head outer surface and solve the model then we get the natural frequency of assembled model.

Table1 Mode3.1 analysis result

SET TIME/FREQ

LOAD STEP

SUBSTEP

CUMULATIVE

1 20.015 1 1 1 2 21.254 1 2 2 3 22.591 1 3 3 4 25.001 1 4 4 5 28.47 1 5 5 6 30.197 1 6 6 7 33.619 1 7 7 8 36.885 1 8 8 9 43.098 1 9 9

10 55.847 1 10 10 11 32.837 1 11 11 12 65.423 1 12 12 13 76.485 1 13 13 14 79.123 1 14 14 15 81.259 1 15 15 16 86.906 1 16 16 17 96.776 1 17 17 18 100.3 1 18 18 19 112.36 1 19 19 20 130.37 1 20 20

The table3.1 represents model analysis results and in this model analysis we took 20 mode shapes. The 20 mode shapes satisfied the participation factor. The fig.3.3 to 3.6 represents different mode shapes analysis of airframe section. Hence we observe in this modal analysis one of the worst case was at mode shape 17 and the frequency at that mode was 96.77Hz. If our model working frequency more that that frequency, with in fraction of time to cross that worst case of that frequency. And some are critical at mode shapes 9, 10 and15 so at this frequencies the above manner with in fraction of time to cross that frequencies.

Page 3: RANDOM VIBRATION ANALYSIS OF AEROSPACE …ipasj.org/IIJME/Volume3Issue2/IIJME-2015-01-24-1.pdf · Random vibration analysis of an equipped section of ... “Introduction to Random

IPASJ International Journal of Mechanical Engineering (IIJME) Web Site: http://www.ipasj.org/IIJME/IIJME.htm

A Publisher for Research Motivation........ Email: [email protected] Volume 3, Issue 2, February 2015 ISSN 2321-6441

Volume 3, Issue 2, February 2015 Page 3

4. Spectrum Analysis and Results & Discussions

0

0.005

0.01

0.015

0.02

20 100 1000 2000

PSD

(g^2

/Hz)

Frequency (Hz)

Acceleration PSD curve

Fig 4.1 Input PSD curve

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IPASJ International Journal of Mechanical Engineering (IIJME) Web Site: http://www.ipasj.org/IIJME/IIJME.htm

A Publisher for Research Motivation........ Email: [email protected] Volume 3, Issue 2, February 2015 ISSN 2321-6441

Volume 3, Issue 2, February 2015 Page 4

The above figure 4.1 represents input acceleration PSD curve. The frequency range 20-2000Hz and corresponding PSD values are shown in above figure.

Page 5: RANDOM VIBRATION ANALYSIS OF AEROSPACE …ipasj.org/IIJME/Volume3Issue2/IIJME-2015-01-24-1.pdf · Random vibration analysis of an equipped section of ... “Introduction to Random

IPASJ International Journal of Mechanical Engineering (IIJME) Web Site: http://www.ipasj.org/IIJME/IIJME.htm

A Publisher for Research Motivation........ Email: [email protected] Volume 3, Issue 2, February 2015 ISSN 2321-6441

Volume 3, Issue 2, February 2015 Page 5

Table 4.1 Analysis results compare with Experiment results

The above figures from 4.2 to 4.10 represents airframe section PSD values in the form of PSD (g^2/Hz). Those values were calculated in terms of grms by using following relations. Each figure represents each one component of airframe section of aerospace vehicle.

0

2

4

6

8

10

12

I II III IV V VI VII VIII IX

Analysis results

Experime ntal resuls

grms(Root mean square of

acceleration)

Airframe sectioncomponents locations

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IPASJ International Journal of Mechanical Engineering (IIJME) Web Site: http://www.ipasj.org/IIJME/IIJME.htm

A Publisher for Research Motivation........ Email: [email protected] Volume 3, Issue 2, February 2015 ISSN 2321-6441

Volume 3, Issue 2, February 2015 Page 6

In the above figure X-axis represents component locations in airframe section and Y-axis represents the vibration level (grms) value of components for a given input. The above figure shows the comparison of experimental results with analytical results. When compared both experimental and analysis results, there was a close relation between them. At location I, location II, location IV, and location V components were in good agreement, Fig.4.11. At location VII, location VIII, and location IX components were close. Much variation has been observed for location III and location VI components.

The reasons are discussed below for variation at output results in the components of airframe section when compare both experimental and analysis results. The airframe section of aerospace vehicle is fixed at twelve locations with bolts and nuts in experiment, but in

analysis the airframe section was constrained with all degree of freedom at complete circumference of bottom outer surface.

During experimentation it is possible to locate the exact center of gravity where as in analysis locates of center of gravity is by geometry (Approximation).

Accuracy of analysis results depends on element size and mesh quality. Presences of cables were considered in experimentation, were as they were not considered in analysis.

5.CONCLUSIONS Based on the work carried out, the following conclusions are made. An airframe section of Aerospace vehicle was subjected to spectrum (PSD) analysis and the results are validated

with experimental results. For modal analysis 20 mode shapes and 20 natural frequencies were find out of which some natural frequencies are

critical. Random vibration response was found experimentally at 9 locations. And in analysis we conducted spectrum (PSD)

analysis and found random vibration response at 9 locations of air frame section components with same parameters and validated with the experimental results.

Experimental results shows close agreement compared to analysis. Finally we conclude that the analysis results give good approximation to experimental results, resulting in reduced cost of the project and product development time repetitively with the requirement of no special setup.

REFERENCES [1] N.C. Nigam, “Introduction to Random Vibrations (Structural Mechanics)” – October 13, 1983, [2] N.C. Nigam, S. Narayanan, “Applications of Random Vibrations” – 9 Dec 1994 [3] Response Spectrum results for the standard mono, G.Houghton; B Fell [4] Karlin, Samuel & Taylor, Howard M. “An Introduction to Stochastic Modeling”, [5] Newland.D.E., “An Introduction to Random Vibrations, Spectral and Wavelet Analysis, Third Edition” [6] Crandall, S., Mark, W., “Random Vibration in Mechanical Systems”, Academic Press, New York (1963). [7] Robson, J. D., (1964), “An Introduction to Random Vibration”, Edinburgh University Press, Edinburgh. [8] Steinberg, D.S., “Vibration Analysis for Electronic Equipment,” John Wiley & Sons Inc., 2000. [9] ANSYS classic Mechanical structural, model and dynamic analysis in ANSYS 14.5. [10] Altair Hyper Works 12.0. Help and guide lines

AUTHOR Durga Prasad Gopalam received the B-Tech degrees in Mechanical Engineering from Vardhman college of Engineering & Technology in 2011 and M.E. Machine Design in Sir C.R .Reddy college of Engineering in 2015. Dr. K. Lalit Narayan professor, Department of Mechanical Engineering Sir C.R.Reddy college of Engineering, Eluru.