DOI : 10.17577/IJERTV3IS111128
- Open Access
- Total Downloads : 298
- Authors : Narra. Tilak Ratan , Dr G. Vijay Kumar , Smt M. Rajya Lakshmi
- Paper ID : IJERTV3IS111128
- Volume & Issue : Volume 03, Issue 11 (November 2014)
- Published (First Online): 28-11-2014
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License:
This work is licensed under a Creative Commons Attribution 4.0 International License
Experimental Investigation on Natural Frequency of Poly Propylene Beam with Crack
Narra.Tilak Ratan PG Student,
Department of Mechanical Engineering, PVP Siddhartha Institute of Technology, Vijayawada.
Dr G. Vijay Kumar Professor,
Department of Mechanical Engineering, PVP Siddhartha Institute of Technology, Vijayawada.
Smt M. Rajya Lakshmi Assistant Professor,
Department of Mechanical Engineering, PVP Siddhartha Institute of Technology, Vijayawada, A.P.
Abstract- Poly Propylene is one of the materials which is used in several applications like home appliances, car bodies, agriculture, home construction, etc. Cracks may be occurring at time of manufacturing, assembly or usage, thus results in reduced stiffness. So, there is a need to recognize damage which may be affecting other parts of the system also. There are various methods to recognize cracks. Natural frequency analysis is one of the better method to analyze cracks because frequency dependent on stiffness of the material. In this article, natural frequency of Poly Propylene beam is analyzed in cantilever condition with two cracks of different depth to width ratios using ANSYS-14.5 and then the results are compared with experiment. Effect of Nano Clay is analyzed with different percentages of Nano Clay. It is observed that addition of Nano Clay improves stiffness of the material.
Keywords Poly Propylene Beam, Natural frequency analysis, Experimental work, Nano Clay.
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INTRODUCTION
Poly Propylene is a semi-crystalline thermo plastic that is used extensively due to its unique combination of properties, cost and ease of fabrication. All grades consist of polymer, a neutralizer and antioxidants. Other additives like clarifiers, nucleates, slip additives, UV stabilizers, silica, talc, and calcium carbonate are added to impart specific functionality. The polymer may be a pure homo polymer made by polymerizing propylene, a random copolymer made from propylene and another monomer (like ethylene), or an impact copolymer made by dispersing rubber in polypropylene matrix. The main advantages of Poly Propylene are, high chemical and corrosion resistance, light weight and rigid, high tensile strength, excellent abrasion resistance, low moisture absorption, easily machined and cut, easy to maintain and clean, excellent thermal insulating properties, excellent dielectric properties, long life span. So, these are mostly used in home appliances, car bodies, chemical industries, agriculture, home construction etc. Damages may be occurring at time of manufacturing or assembly or usage, thus resulting in reduced stiffness and then component would become useless.
They are many non destructive tastings are there like acoustic emission testing, blue etch anodize, dye penetrate inspection, liquid penetrate testing, electromagnetic testing, ultrasonic testing, vibration analysis, visual inspection etc. to detect crack. Vibration analysis is mostly better and suitable technique among all of techniques. In this method, impact hammer is used to create vibration of the beam and laser vibro meter is used to receive output frequency of the beam. Dimensions are taken as, 0.8X0.05X0.006 m3 and followed by standard in [19].
The introduction of nanofiller in the polymer nano composites had proved a significant improvement in the mechanical properties. The addition of small amounts of clay (0 to 15% wt) in a polymer matrix leads to improved mechanical, thermal and barrier properties. The addition of Nano Clay in a polymer matrix may result in the formation of two types of Nano Composite Structures, namely, intercalated and exfoliated nanostructures. In an intercalated structure, the host polymer matrix enters into the interlayer spacing of the Nano Clay and increases the interlayer spacing but maintains the parallel arrangement of the nano layers of clay in the matrix. In practice, exfoliated structures provide enhanced and improved properties due to their excellent dispersions and improved aspect ratio.
In this paper, efforts have been going made through PP beam for cracked with different crack to depth ratios by simulation and experimental basis.
Material properties of PP material as, E=1.35X109 N/m2, poisons ratio=0.4,Density=905 Kg/m3 and Nano Clay as, E=7.016X109 N/m2 , poisons ratio =0.017, Density= 163.6 Kg/m3
Steps involved in extrcting frequencies of cracked beam main steps involved to detect frequencies of cracked beam are,
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Natural frequency of un-cracked beam for Poly Propylene material is determined theoretically.
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Natural frequency of un-cracked beam for Poly Propylene material is estimated in ANSYS and is compared with theoretical results.
Vol. 3 Issue 11, November-2014
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Natural frequencies of Poly Propylene material are estimated for different crack depths by using ANSYS.
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Natural frequencies of Poly Propylene material are estimated experimentally for different crack depths and compared with ANSYS results.
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Effect of Nano Clay was analyzed by using ANSYS for different crack depths for different percentages of NC by following same steps 1, 2 and 3.
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THEORETICAL CALCULATIONS FOR UN-CRACKED
PP BEAM
Theoretical formulae were obtained from [20] for four modes of natural frequencies. Results obtained by the formulas as,
Natural frequency of 1st mode=1.85Hz. Natural frequency of 2nd mode=11.57Hz Natural frequency of 3rd mode=32.45Hz Natural frequency of 4th mode=63.65Hz
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FINITE ELEMENT MODELING FOR UN-CRACKED PP
BEAM
The ANSYS finite element software is used for free vibration of the cracked beams. A 20-node three- dimensional structural solid element under SOLID 186 is selected to model the beam. The beam is discredited into 1045 elements with 2318 nodes. Geometrical shape of the beam is shown in figure 1.Cantilever boundary condition is considered by constraining all degrees of freedoms of the nodes located on the left end of the beam. The subspace mode extraction method is used to calculate the natural frequencies of the beam and mode shapes are shown in figure 2.
Figure 1 : Geometrical model for un-cracked beam
2-a: 1st mode-1.8629Hz frequency
2-b: 2nd mode-11.607Hz frequency
2-c: 3rd mode-32.629Hz frequency
2-d: 4th mode-64.0589Hz frequency Figure 2: Mode Shapes of un-Cracked PP Beam
IV . COMPARISON OF THEORETICAL RESULTS WITH ANSYS 14.5 RESULTS
After comparison of both theoretical and ANSYS results, the difference between both results is negligible and comparison of frequency is shown in figure 3. Hence, the analysis of cracked beam is extended in ANSYS package.
70
60
50
40
30
20
10
0
Theoritical results
ANSYS
Results
frequency (Hz)
Figure 3: Comparision of theoritical frequency with ANSYS
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Results for PP Beam with Crack
After comparison of the both theoretical and ANSYS results, Procedure could be verified in ANSYS
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for Aluminum material. Same results were obtained from that procedure. Hence, the same procedure is adopted for extracting natural frequencies and % of decrees in frequency of cracked beam as shown in figure 4 and 5 and obtained results are listed in table 4.The percentage of variation for different mode frequencies with varying crack depth is shown in figure 6.
Figure 4: Location of cracks on composite beam
Figure 5: Geometrical model of crack.
4th mode
3rd mode
2nd mode
1st mode
4th mode
3rd mde
2nd mode
Table 4: Natural frequencies and percentage of decrease in frequency of beam for different cracks depths
frequency(Hz)
% of variation of frequency
1st mode
0
1.8629
64.0589
—
—
0.25
1.84721
63.849
0.842235
0.327667
0.5
1.78451
63.027
4.207955
1.610861
0.75
1.53245
11.266
30.7274
60.206
17.73847
3.467658
5.972031
6.014621
1.276661
0.733461
32.2618
11.5851
0.242663
0.138809
32.5997
11.6545
—
—
32.679
11.6707
Percentage of
decrease in frequency
20
15
10 a/w=0.25
5
0 a/=0.5
a/w=0.75
Figure 6: percentage of variation in frequency for crack depth
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EXPERIMENTAL RESULTS
The poly propylene material is imported from Polyester polymers, Mumbai. Specimens were prepared by using different operations as, cutting, finishing. And cracks were created by using mini hack saw blade. Vibration testing was done by using Impact Hammer, Laser Vibro meter and Data acquisition System. The schematic diagram for experimental set up is shown in figure 7 and experimental setup is shown in figure 8,9.
Figure 7: Schematic diagram for experimental setup.
Figure 8: Experimental setup.
Figure 9-a: Fixed boundary condition
Figure 9-b: Impact action Figure 9-c: Leaser incidence Figure 9: Experimental work.
Frequency (Hz)
The experimental results are correlated with ANSYS results as shown in figure 10.
70
60
50
40
30
20
10
0
1st mode-experimental
2nd mode-experimental 3rd mode-experimental 4th mode-experimental 1st mode-ANSYS
2nd mode-ANSYS
1 2 3 4
Crack Depth to width(a/w) ratio
3rd mode-ANSYS
4th mode-ANSYS
Figure 10: Comparison Of Experimental Results With ANSYS Results Effect Of NC
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Analysis of Effect of Nano Clay
The mechanical properties of Poly Propylene-Nano Clay are listed in table 5. The material properties of Poly Propylene with Nano Clay addition is obtained through rule of mixtures. Frequency response results of different crack depths for different compositions of Nano Clay are obtained and are listed in table 6. Comparison of results is shown in figure 11.
Table 5 : Properties of PP-NC Composite Material By Rule of Mixes
S.No
%
0f
NC
E for composite (N/m2)
poisons ratio
for composite
Dennsity of mixtre (Kg/m3)
1
0
1.35E+09
0.4
905
2
3
1.52E+09
0.322
882.758
3
7
1.74E+09
0.333
853.102
4
11
1.96E+09
0.403
823.446
5
15
2.18E+09
0.369
793.79
%
of NC
a/w
Frequency(Hz)
1st mode
2nd mode
3rd mode
4th mode
0
0
1.863
11.67
32.68
64.06
0.25
1.847
11.65
32.6
63.85
0.5
1.785
11.59
32.26
63.03
0.75
1.532
11.27
30.73
60.21
3
0
1.996
12.61
35.02
68.62
0.25
1.979
12.49
34.93
68.39
0.5
1.908
12.41
34.64
67.46
0.75
1.607
12.06
32.81
64.84
7
0
2.173
13.62
38.12
74.71
0.25
2.155
13.6
38.03
74.47
0.5
2.09
13.53
37.67
73.7
0.75
1.774
13.13
35.74
70.01
11
0
2.354
14.74
41.29
80.93
0.25
2.335
14.72
41.19
80.67
0.5
2.255
14.64
40.76
79.63
0.75
1.937
14.23
38.82
76.06
15
0
2.525
15.82
44.29
86.81
0.25
2.501
15.8
44.18
86.53
0.5
2.416
15.7
43.71
85.38
0.75
2.068
15.26
41.58
81.5
Table 6 : Results of PP-NC Composite material for different crack depths
First Mode
3
2
1
0
0 0.25 0.5 0.75
0% Nano
Clay
3% Nano Clay
7% Nano
Crack depth to width (a/cwla)yratio
Second Mode
20
15
10
5
0
0 0.25 0.5 0.75
0% Nano
Clay
3% Nano Clay
7% Nano
Crack depth to width (ac/lway) ratio
Third Mode
60
40
20
0
0 0.25 0.5 0.75
0% Nano
Clay
3% Nano Clay
7% Nano
Crack depth to width (ac/lway) ratio
Fourth Mode
0% Nano
Clay
3% Nano Clay
7% Nano
Crack depth to width (cala/wy ) ratio
50
0
100
Frequency(Hz)
Frequency(Hz)
Frequency(Hz)
Frequency(Hz)
Figure 11: Comparisons of frequency with change in Nano Clay and crack depth ratio
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CONCLUSIONS
After analyzing the natural frequencies of Poly Propylene beam and effect of Nano Clay, following conclusions are made.
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Frequency response of beam decreases with increase in crack depth Because of decrease in stiffness.
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Percentage of decrease in frequency is too high for 0.75 crack depth to width ratio indicates very lagging in stiffness of the beam. Finally that may be become useless.
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Frequency response of beam increases with increase in Nano Clay percentage indicates Nano Clay could be improved stiffness of material according to frequency analysis.
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Decrease of frequency is all most same for same any combination of poly Propylene-Nano Clay material for same crack depth to width ratio.
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