THEORETICAL MODEL DESIGN OF A HIGH MASS MECHANICALLY DAMPED VIBRATIONAL SYSTEM

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1 International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 9, September 2017, pp , Article ID: IJMET_08_09_020 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed THEORETICAL MODEL DESIGN OF A HIGH MASS MECHANICALLY DAMPED VIBRATIONAL SYSTEM M Tech - N I T Calicut, Assistant Professor, Mechanical Engineering College of Engineering and Management, Punnapra, India ABSTRACT The three types of vibratory motion are carried out in a Vibrational system and its design factors were also considered. Force transmitted is more than force applied. Maximum amplitude of vibration was found out to be 2mm.Thus a satisfactory vibration system model is defined using basic set of equations of vibratory motion. Finally the Vibratory motion is being damped using a damping system. Key words: Vibration system. Cite this Article:, Theoretical Model Design of a High Mass Mechanically Damped Vibrational System, International Journal of Mechanical Engineering and Technology 8(9), 2017, pp INTRODUCTION When external forces are applied to bodies such as a spring, a beam or a shaft, they get displaced from the equilibrium position by the application of external forces. When a body is stretched, the internal forces in the form of elastic or strain energy are present in the body. At release, these forces bring the body to its original position. When the body reaches the equilibrium condition, the strain energy is converted to kinetic energy so that stretched body continues to move in the opposite direction. Then again it attains equilibrium position by converting again kinetic energy into strain energy. Thus a vibratory motion is repeated successively. There are three types of vibratory motion in a vibrational system. When no external force acts on a body after giving it an initial displacement, then it is free or natural vibrations. When the similar body is said to vibrate under external force, it is forced vibration. When finally there is reduction in amplitude over every cycle of vibrations, the motion is finally damped vibrational motion editor@iaeme.com

2 When a body is displaced from its equilibrium position by an external force and released, the body starts vibrating. The external forces may be due to the dynamically unbalanced masses in the rotating machines. The external force applied to the system is periodic in nature. The energy possessed by a vibrating system is gradually dissipated in overcoming friction and other resistances. Natural frequency is the frequency of a system having free vibrations. It is equal to (1/2π) (g/δ) Resonance is the condition in which the external exciting force coincides with the natural frequency of the system. There are three types of free vibrations. They are longitudinal vibration, Transverse vibration and Torsional vibration. When the particles of the shaft moves parallel to the axis of the shaft, it is called as longitudinal vibration. When the particles of the shaft move approximately perpendicular to the axis of the shaft, it is called transverse vibration. When the particles of the shaft move in a circle about the axis of the shaft, it is called torsional vibration. Figure 1 2. DESIGN OF A VIBRATIONAL SYSTEM Consider a vibrational system in which the three types of motion are employed. Here the system consists of a shaft of mass m=2000kg when one end is fixed. Let s= stiffness of the shaft δ=static deflection due to weight of the body x=displacement of body from mean position after time t editor@iaeme.com

additional deflection be y So m d²x/dt² = S(y-x) m/s (d²x/dt²) +x = y Figure 2

3 Theoretical Model Design of a High Mass Mechanically Damped Vibrational System m=mass of body=w/g The governing equation of this system is md²x/dt² = -Sx Let additional deflection be y So m d²x/dt² = S(y-x) m/s (d²x/dt²) +x = y Figure 2 3. SYSTEM DESIGN Figure editor@iaeme.com

4 md²x/dt² = S(y-x) m/s(d²x/dt²) + x=y x=a sin (s/m)t +B cos (s/m)t +y/(1-(2π/ (s/m))² ω = 2πf =2π 18.3rad/s ω = (s/m) ω²m = s s= mg/δ δ = /(37π)² 2000 When t=0, x=0, y is a function of t then, B=0 x= Asin (((37π)² 2000)/2000) /(1-(2π/ ((37π)² 2000)/2000 = = 1.254m F= mω²r = kn ωn =2πfn fn = 1/2π( g/δ) =19.98Hz ωn=126 rad/s ω=115rad/s ϵ = 1/(1-(ω/ωn)² =1/0.16 =6.25 FT=F ϵ = =62.5kN Sxmax =62.5 Xmax=0.002m Maximum Amplitude of Vibration is equal to 2mm. 4. CONCLUSIONS The three types of vibratory motion are carried out in a Vibrational system and its design factors were also considered. Force transmitted is more than force applied. Maximum amplitude of vibration was found out to be 2mm.Thus a satisfactory vibration system model is defined using basic set of equations of vibratory motion. Finally the Vibratory motion is being damped using a damping system. REFERENCES [1] Online Model Recursive Identification for Variable Parameters of Driveline Vibration: Pelin Dai, Ying Huang,Dinghao Hao,Ting Zhang, SAE International, [2] Optimization of Vibration Performance and Emission of C.I Engine Operatedon Sinarouba Bio diesel using Taguchi and multiple Regression Analysis: Dnyaneshwar. V.Kadam Sangram.D.Jadhav editor@iaeme.com

5 Theoretical Model Design of a High Mass Mechanically Damped Vibrational System [3] SAE International, [4] Measurement of Engine Vibrations with a fuel blend of Recycled lubricating Oil and Diesel Oil:Marcos Gutierrez, Andres Castillo, Juan Inignez, Gorkey Reyes, SAE International, [5] In-Plane and Out of Plane Vibrations of Brake linings on the rotor: Georg Peter Ostermeyer,Johannes Otto,Seong Kwan Rhee,SAE International, [6] Systematic Experimental Creep Groan Characterization using a Suspension and Brake Test Rig:Manuel Purscher,Peter Fischer, SAE International, [7] Reduction of Driveline Boom Noise and vibration of 40 seat Bus through Structural Optimization: [8] Jose Frank,Sohin Doshi,Manchi Rao, Prasath Raghavendran, SAE International, [9] Theory of Machines: R.S.Khurmi, J.K.Gupta, S.Chand Publications [10] The Condition Monitoring of Rolling Element Bearings using Vibration Analysis: J.Mathew and R.J.Alfredson, ASME Journal, ,July01,1984 [11] Mechanical Vibrations: Singires S Rao, Pearson Education India [12] Text Book of Mechanical Vibrations: Rao. V.Dukkipati, J.Srinivas, PHI Publications [13] Arundhati Garad and Prof. V. J. Shinde. A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects on Vibrations. International Journal of Mechanical Engineering and Technology, 8(6), 2017, pp [14] D. Rajesh, V. Balaji, A. Devaraj and D. Yogaraj. An Investigation on Effects of Fatigue Load on Vibration Characteristics of Woven Fabric Glass/Carbon Hybrid Composite Beam under Fixed-Free End Condition using Finite Element Method. International Journal of Mechanical Engineering and Technology, 8(7), 2017, pp editor@iaeme.com

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DYNAMIC ANALYSIS OF ROTOR-BEARING SYSTEM FOR FLEXIBLE BEARING SUPPORT CONDITION International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 7, July 2017, pp. 1785 1792, Article ID: IJMET_08_07_197 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=8&itype=7