1. Linseed oil + Styrene + Divinylbenzene
Figure 3: Schematic of test piece for forced vibration test
New Test Methodology for determining Damping Loss Factor of Polymers using Vibration Response Method
Rakesh Das1, Rajesh Kumar2, P. P. Kundu*1
1Department of Polymer Science and Technology, University of Calcutta, 92, A.P.C. Road, Kolkata , India
2Precision Metrology Laboratory, Department of Mechanical Engineering, Sant Longowal Institute of Engineering & Technology, Sangrur, Punjab , India
Elastomeric materials are ideal vibration dampers and their performance is defined by loss factor.
Dynamic mechanical analyzer (DMA) is the most powerful tool for determining the loss factor of the material.
From vibration response test, one can evaluate loss factor. The forced vibration and free vibration principle can be utilized in experiments and analysis.
Thus we have fabricated a low cost vibration testing experimental set up
Objectives:
Development of a new low cost testing system for evaluation of damping property of polymer. in the simplest way
The performance optimization of this testing system by comparing the results obtained from this system with the r dynamic mechanical analysis results.
In free oscillation method , the decay of amplitude of vibration generated by an impulse of excitor is expressed in terms of logarithmic decrement (δ),
Logarithmic decrement, (1)
{ where A is peak to peak amplitude of the ith peak and Ai+r is the ( i+r)th peak of the time decaying curve}
Or the damping ratio may be expressed as , (2)
In case of low damping (typically, ζ< 0.1), then , the equation (1) becomes
(3)
The loss factor (4)
In forced vibration cantilevered sandwiched beam vibration is analyzed according to ASTM E
To validate the experiment Young’s Modulus and loss factor of base layer material of the was deduced from the equation
(5)
(6)
[Where, is the resonance frequency and is the bandwidth , calculated from the resulting wave form is the coefficient of the nth mode, is the density of the base beam, is the length of the beam and H is the thickness of the beam in the vibration direction]
The shear loss factor of the elastomers are given by
(7)
Where,
[ = density of the elastomeric
material ]
= resonance frequency for mode s of sandwiched beam, =half power bandwidth of mode s of composite beam
= thickness ratio [ is the thickness of the elastomeric materials] s = index number: 1, 2, 3 and s=n,
Description and preparation of test material:
The test materials are elstomers synthesized from linseed oil through cationic polymerization techniques.
Linseed oil + Styrene + Divinylbenzene
Stage I
0o C
BF3 OEt2
Stage II
room temp
12 h
60o C
Stage III
Stage IV
110o C
24 h
Final polymer sample
120o C
3 h
Figure 4: Image of test piece for free vibration test
Introduction:
Methodology:
Fabrication of experimental set up.
Preparation of test piece.
Evaluation of damping loss factor applying free vibration and forced vibration principle.
Mathematical Analysis for free vibration test:
Figure: 2 Experimental set up for free vibration test
Figure: 1 Schematic of experimental set up for forced vibration test
Mathematical Analysis for forced vibration test:
Results & Discussion:
Table 1: Results obtained from vibration response method and its comparison with DMA a
Test material
Loss factor in tensile mode from DMA at 5 Hz frequency
Loss factor in shear mode from forced vibration test
Loss factor from free vibration test at 5 Hz frequency
Sample 1
0.57
0.24
0.46
Sample 2
0.82
0.32
0.73
Sample 3
0.96
0.48
0.85
Conclusion:
A new testing system for determining the damping loss factor of the polymer has been developed.
The performance of the testing system was verified through evaluation of damping loss factor of elastomer synthesized from linseed oil.
The results obtained from this system are compared with results from dynamic mechanical analysis test and the results are in good agreement.
In the time decay curve the peak to peak (p-p) amplitude of excitation (Ai) is decayed within a cycle because of high damping property of the elastomeric material.
The amplitude (p-p) of excitation (Ai) and amplitude after decay(Ai+r) are noted to calculate logarithmic decrement (δ) using equation (4).
The damping ratio (ζ), loss factor (η) are calculated for each sample from this logarithmic decrement value (δ) using equation (6) and equation (7).
The results from free vibration test have good agreement with the results from dynamic mechanical analysis.
In forced vibration the vibration response of the test materials are observed under 1 Hz to 1 KHz sweep of sine wave having amplitude 500 mV (R.M.S). The loss factor is calculated at the natural frequency of the system in 2nd mode which is in the range of 200 Hz to 300 Hz. In this higher frequency range the loss factor value diminishes. b
Acknowledgement:
The financial support under major research project scheme (F.No (2008) (SR)) from University Grant Commission (UGC), New Delhi, India is highly acknowledged.
Figure 5: Vibration response of sample 1 (a) in free vibration (b) forced vibration