modal and harmonic-response analysis of two … · modal and harmonic-response analysis of two...

DOI:10.23883/IJRTER.2018.4241.79JUO 298

MODAL AND HARMONIC-RESPONSE ANALYSIS OF TWO

WHEELER CONNECTING ROD USING 3 DIFFERENT

MATERIALS

Gangadhar R.Patil1, Prof. A.C.Mattikalli2 1M.Tech. Mechanical Engg. Dept, MMEC, Belagavi

2Assistant Prof. Mechanical Engg. Dept, MMEC, Belagavi

Abstract— The main objective of this project is to determine the mode shape, natural frequency

[Hz], dynamic behavior response of connecting rod under each frequency in terms of harmonic

stress, harmonic deformation for three different material connecting rods like structural steel [A-36],

aluminium alloy [T6-6061] and grey cast iron [HT-250] for selection purpose in 155cc Suzuki

Gixxer SF motorcycle. 3D modelling of connecting rods is carried out using CAD software like

Unigraphics NX8.5 and simulation is carried out using FEA software, like Ansys Workbench V15.

In this simulation software we are performing modal analysis and harmonic-response analysis for all

three connecting rods. The boundary condition is also applied on the basis of its working principle.

Thus connecting rods are subjected to different loading conditions due change in the mass as per

design condition. Modal and harmonic-response analysis helps in finding the resonant frequency of

the connecting rod. This analysis is most accurate.

Keywords— Modal analysis; Harmonic-response analysis; Ansys WorkbenchV15; Unigraphics

NX8.5; Connecting rod;

I. INTRODUCTION The main function of connecting rod is to convert reciprocating motion of the piston into rotary

motion of the crank, as well as responsible for transferring power from the piston to the crankshaft

and sending it to the transmission.

Modal analysis is a mode-superposition method, which produce natural mode shapes and natural

frequencies of connecting rod under free vibration condition without application of any load. The

mode shapes describes the displacement or deformation of an object and permit the design to vibrate

at a specified frequency and also describe the mass participation factor in each mode.

Harmonic Response, there is application of continuous load on the connecting rod under forced

vibration condition. Where it provides the dynamic behavior response of connecting rod under each

frequency level. Also helps in finding the resonant frequency of the connecting rod.

II. OBJECTIVE

Selection of suitable connecting rod for 155cc Suzuki Gixxer SF motorcycle. 3D modelling is carried

out in Unigraphics NX8.5 and simulation is carried out in Ansys WorkbenchV15 software. Perform

modal analysis and harmonic-response analysis for all three connecting rods. Determine the natural

mode shapes and natural frequencies of connecting rod. Check the dynamic behavior response of

connecting rod under each frequency [Hz].

III. MATERIAL SELECTION

In this project, there are totally 3 different materials taken into account for the production of

connecting rod.

International Journal of Recent Trends in Engineering & Research (IJRTER) Volume 04, Issue 04; April - 2018[ISSN: 2455-1457]

@IJRTER-2018, All Rights Reserved 299

3.1. Structural steel – ASTM grade [A-36]

It is mild steel containing low carbon percentage, easy to machining, fabricate and securely welded.

It provides good strength and high ductility. This is available in rectangle bar, square bar circular rod

and steel shapes such a channels, angles, H-beams and I-beams form.

Table 1. Chemical composition Table 2. Mechanical properties

Elements Contents

Properties Metric

[S.I unit]

Iron (Fe) 98% Density 7850 [kg/ m3]

Carbon (C) 0.25 – 0.29% Young’s modulus 2.1E+5 [MPa]

Copper (Cu) 0.20% Poisson’s ratio 0.3

Manganese (Mn) Max 1.03% Rockwell hardness 68 [HRB]

Phosphorus (P) Max 0.04% Tensile yield strength 250 [MPa]

Silicon (Si) 0.28% Ultimate tensile strength 400 [MPa]

Sulphur (S) Max 0.05% Melting point 1425 - 1540 [oC]

3.2. Aluminium alloy – ASM grade [T6-6061] It is a versatile heat treatable extruded alloy with medium high strength capability material. In this

T6 term represents solution heat treated and artificially aged. Light weight and provides good surface

finish. It is available in tube, bar, pipe and rod form.


Elements Contents

Properties Metric

[S.I unit]

Aluminium (Al) 95.8 – 98.6% Density 2770 [kg/ m3]

Chromium (Cr) 0.04 – 0.35% Young’s modulus 0.71E+5 [MPa]

Copper (Cu) 0.15 – 0.40% Poisson’s ratio 0.33

Manganese (Mn) Max 0.15% Rockwell hardness 95 - 97 [HRB]

Silicon (Si) 0.4 -0.8% Tensile yield strength 280 [MPa]

Iron (Fe) Max 0.7% Ultimate tensile strength 310 [MPa]

Magnesium (Mg) 0.8 – 1.2% Melting point 580 - 650 [oC]

Titanium (Ti) Max 0.15%

Zinc (Zn) Max 0.25%

3.3. Grey cast iron – grade [HT-250]

It is a type of cast iron, having graphitic microstructure with low cost and good machinability, which

result from the graphite lubricating the cut and breaking up the chips. Having good damping capacity

to absorbs the energy and converts it into heat.


Elements Contents

Properties Metric

[S.I unit]

Iron (Fe) 89% Density 7200 [kg/ m3]

Carbon (C) 3 – 3.3% Young’s modulus 1.26E+5 [MPa]

Graphite (Gr) 6 – 10% Poisson’s ratio 0.26

Silicon (Si) 1.4 – 1.7% Brinell hardness 190 [HBS]

Manganese (Mn) 0.8 – 1% Ultimate tensile strength 240 [MPa]

Phosphorus (P) 0.15% Ultimate compressive strength 820 [MPa]

Sulphur (S) 0.12% Melting point 1200 – 1400 [oC]



IV. SPECIFICATION AND LOADING CONDITION OF CONNECTING ROD

4.1. Configuration of Suzuki gixxer SF model

Considering 155cc engine,

Engine type - Air cooled, 4-stroke, having

Bore, B or Piston diameter, D = 56 mm

Stroke, S = 62.9 mm

Number of Cylinders, n = 1

Displacement = 154.9 cm3 i.e. [π/4*B2*S*n]

Length of connecting rod, L = 2 * stroke of piston= 2 * 62.9 = 125.8mm

Maximum Power, P = 14.8 bhp at 8000 RPM

Maximum Torque, T = 14 N-m at 6000 RPM

4.2. Specification of Petrol

Compression Ratio of PETROL [C8H18] = 9.35:1

Density of petrol, ρ = 737.22E-9 kg / mm3

Molecular weight, M = 114.228 g / mole

Ideal gas constant, R = 8.314 J / mol-K

Temperature, T = 27oC+273 = 300 Kelvin (K) [ Ideal room temperature]

From perfect gas equation,

PV = mRspecific T

P = Pressure, V= Volume, m = Mass, T = Ideal room temperature and Rspecific = Specific gas constant

Mass, m = Density * Volume

= 737.22E-9 * 154.9E3

= 0.1142 kg * 9.81= 1.12 N.

Rspecific = R / M

= 8.314 / 0.11422 = 72.79 J / kg.K

Substitute all above values in perfect gas equation, we get

Pressure (P) = 16 MPa or 160 Bar.

4.3. Loading condition

The force on the piston due to gas pressure and Inertia of reciprocating parts which leads to set up

the stresses in connecting rod. With the help of theoretical design calculation method we calculate

the total mass of connecting rods as well as total force acting on the connecting rods. Factor of safety

parameter is considered during the time of design calculation. The net force acting on the piston pin

region in vertical downward direction at the time of power stroke condition. Therefore net load or net

force acts as a compressive load or compression load. The following table gives force values to all 3

different material connecting rods.

Table 7. Compressive force or load acting on the connecting rods

Sl. no Materials

Mass [kg]

Force [N]

1. Structural steel (A-36) 0.240 6802

2. Aluminium Alloy T6-(6061) 0.116 7935

3. Grey Cast Iron (HT-250) 0.160 7587



The following parameters or specifications required to prepare a complete 3D model or geometry of

connecting rod. These values are estimated from design calculation method.

Table 8. Specification of connecting rod

Sl.no Parameters Aluminium

Alloy

Structural

Steel

Grey Cast

Iron

1. Thickness of flange and web of connecting rod [t] 5.5 4.7 4

2. Width of the section [B= 4t] 22 19 16

3. Height of the section [H=5t] 28 24 20

4. Height at the big end H1= [1.1H - 1.125H] 31 26 22

5. Height at the small end H2= [0.75H – 0.9H] 21 18 15

6. Inner diameter of small end 40 40 40

7. Outer diameter of small end 50 50 50

8. Length of small end 25 25 25

9. Inner diameter of big end 52 52 52

10. Outer diameter of big end 69 69 69

11. Length of big end 32 32 32

V. 3D MODEL OF CONNECTING ROD

Unigraphics NX8.5 modeling tool is used to create a complete 3D model of connecting rod.

Figure 1. Structural steel grade [A-36] connecting rod Figure 2. Aluminium alloy grade [T6-6061] connecting rod



Figure 3. Grey cast iron grade [HT-250] connecting rod

VI. FEA ANALYSIS OF CONNECTING ROD

Analysis of connecting rod is done through Ansys workbench V14.5 software. Here we are

performing the Modal Analysis, Harmonic-response Analysis for all three materials i.e. Structural

steel [A-36], Aluminium alloy [T6-6061] and Grey cast iron (HT-250).

Modal analysis is helps to determine the mode shape, Natural frequency [Hz] of connecting rods

under free vibration undamped condition.

Harmonic-response analysis is helps to determine the dynamic behavior response of connecting rod

under each frequency in terms of harmonic stress and harmonic deformation. Also helps in finding

the resonant frequency of connecting rod under forced vibration condition.

6.1. Mesh generation





Table 9. Meshing data

Material Elements Nodes Element size Element type Mesh type

Structural steel [A-36] 7489 28983 3 Solid 186, 187 Quad mesh

Aluminium alloy T6-[6061] 6615 27046 3 Solid 186, 187 Quad mesh

Grey cast iron [HT-250] 7625 28642 3 Solid 186, 187 Quad mesh

6.2. Boundary condition

Connecting rod is subjected to compressive load or force about 6802N, 7935N and 7587N in

downward ‘Z’- direction on piston pin end region and all DOF [Degree of freedom] is fixed at crank

end region.

6.2.1. Modal boundary condition





6.2.2. Harmonic-response boundary condition





6.3. Analysis result

6.3.1. Modal analysis

Structural steel [A-36] material connecting rod

Figure 13. 1st mode shape contour of connecting rod Figure 14. 2nd mode shape contour of connecting rod

Figure 15. 3rd mode shape contour of connecting rod Figure 16. 4th mode shape contour of connecting rod

Figure 17. 5th mode shape contour of connecting rod Figure 18. 6th mode shape contour of connecting rod



Aluminium alloy [T6-6061] material connecting rod






Grey cast iron [HT-250] material connecting rod






6.3.2. Harmonic-response analysis

Structural steel [A-36] material connecting rod

Graph 1. Harmonic stress [MPa] Vs Frequency [Hz] in Z –direction

Graph 2. Harmonic deformation [mm] Vs Frequency [Hz] in Z – direction

Aluminium alloy [T6-6061] material connecting rod

Graph 3. Harmonic stress [MPa] Vs Frequency [Hz] in Z - direction



Graph 4. Harmonic deformation [mm] Vs Frequency [Hz] in Z - direction

Grey cast iron [HT-250] material connecting rod

Graph 5. Harmonic stress [MPa] Vs Frequency [Hz] in Z – direction

Graph 6. Harmonic deformation [mm] Vs Frequency [Hz] in Z – direction



VII. VALIDATION

7.1. Calculation of natural frequency of connecting rod

For Structural steel (A-36) material,

Natural frequency,

Fn = [1/2π]*[Sqrt (g/δ)] [Hz]

Static deflection, δ = WL/AE [mm] for cantilever beam with axially loaded (compression)

Acceleration, g = 9810 [mm/sec2]

Static deflection, δ = [6802*125.8] / [30706*2.1E+5] = 1.3270E-4 mm.

Substitute deflection and acceleration values in above equation we get,

Natural frequency, Fn = 1/2π [Sqrt (9810/1.3270E-4)] = 1368.41 Hz.

First natural frequency or Fundamental frequency of connecting rod, Fn1 = 1368.41 Hz.

The same procedure is followed for other two materials.

VIII. RESULTS

8.1. Modal analysis Table 10. Structural steel [A-36] Table 11. Aluminium alloy [T6-6061]

Mode Frequency

[Hz]

Time Period

[Sec]

Mode Frequency

Hz]

Time Period

[Sec]

1 1367.1 0.73146E-3 1 1490.1 0.67110E-3

2 1886.6 0.53004E-3 2 1954.2 0.51172E-3

3 2683.4 0.37266E-3 3 2931.8 0.34109E-3

4 6677.4 0.14976E-3 4 6192.1 0.16150E-3

5 6763.4 0.14786E-3 5 6319.5 0.15824E-3

6 7769.8 0.12870E-3 6 7145.4 0.13995E-3

Table 12. Grey cast iron [HT-250]

Mode Frequency

[Hz]

Time Period

[Sec]

1 918.61 0.10886E-2

2 1350.1 0.74070E3

3 1817 0.55035E3

4 5539.7 0.18052E-3

5 5564.4 0.17971E-3

6 6671.3 0.14990E-3

Graph 7. Natural Frequency [Hz] of connecting rod



Table 13. Natural Frequency [Hz] of connecting rod

Sl.no Materials 1st Natural Frequency [Hz]

Ansys result Theoretical result

1. Structural Steel (A-36) 1367.1 1368.41

2. Aluminium AlloyT6-(6061) 1490.1 751.78

3. Grey Cast Iron(HT-250) 918.61 985.53

8.1.1. Modes shape with respect to Frequencies [Hz]

Following are the specific pattern of vibration of a connecting rod to a specific frequency.

Mode -1: In Y-Direction: Bending

Mode -2: In X- Direction: Bending

Mode -3: In Z- Direction: Twisting

Mode -4: In X- Direction: Flipping

Mode -5: In Y-Direction: Tilting

Mode -6: In Z-Direction: Pulling and pushing

8.2. Harmonic-response analysis

Table 14. Harmonic response of Structural steel [A-36]

Mode Frequency

[Hz]

Harmonic Stress

[MPa]

Harmonic Deformation

[mm]

1 1367.1 6.6619 0.0106

2 1886.6 6.8609 0.0110

3 2683.4 7.3312 0.0117

4 6677.4 24.883 0.0399

5 6763.4 26.772 0.0429

6 7769.8 680.74 1.0922

Table 15. Harmonic response of Aluminium Alloy [T6-6061]

Mode Frequency

[Hz]

Harmonic Stress

[MPa]


[mm]

1 1490.1 6.5561 0.0338

2 1954.2 6.7779 0.0350

3 2931.8 7.5415 0.0389

4 6192.1 25.237 0.1302

5 6319.5 29.167 0.1506

6 7145.4 254.62 1.3155

Table 16. Harmonic response of Grey cast iron [HT-250]

Mode Frequency

[Hz]

Harmonic Stress

[MPa]


[mm]

1 918.61 9.7680 0.0256

2 1350.1 9.9917 0.0262

3 1817 10.351 0.0271

4 5539.7 31.033 0.0814

5 5564.4 31.068 0.0830

6 6671.3 202.44 0.5316



From harmonic–response result table, we observed that connecting rod is undergoes peak vibration at

mode number 6 for all three materials. Mode number 6 is the most worst or critical frequency of the

connecting rod because which produce undesirable noise, excessive stresses and also partial or

complete failure of part. But harmonic stress for aluminium alloy and grey cast iron material at mode

number 6 is well below the yield strength. Thus both materials are safe. Maximum damage occurs on

structural steel connecting rod. Hence design of structural steel connecting rod should be carried out

for first five modes only.

IX. CONCLUSION

Harmonic stress at mode number 6 is peak for structural steel connecting rod. Thus maximum

damage or complete failure occurs in structural steel connecting rod.

Design of structural steel connecting rod should be carried out for first five modes only.

Harmonic stress for aluminium alloy and grey cast iron connecting rod is well below the yield

strength for all modes. Hence both materials are safe.

Grey cast iron material connecting rod is selected for its dynamic behavior response i.e. it is

very safe in harmonic stress region.

REFERENCES I. K. Sudershan Kumar, Dr. K. Tirupathi Reddy, Syed Altaf Hussan, “Modeling and Analysis of Two Wheeler

Connecting Rod”, International Journal of Modern Engineering Research, vol-2, Issue-5, Pp-3367-3371, Sep-

Oct-2012.

II. Kuldeep B, Arun L.R, Mohammed Faheem, “Analysis and Optimization of Connecting Rod using Alfasic

Composites”, ISSN: 2319-8753 International Journal of Innovative Research in Science, Engineering and

Technology, vol. 2, Issue 6, June 2013.

III. Santhosh Reddy, “Load Analysis and Multi Body Dynamics Analysis of Connecting Rod in Single Cylinder 4

Stroke Engine”, International Journal for Scientific Research & Development, vol.-3, Issue 08, 2015 | ISSN

(online): 2321-0613.

IV. R.Ravi, B.V Subhramanyam, “Dynamic Load Analysis and Optimization of a Connecting Rod”, IJRMET vol.-

4, April 2014 ISSN: 2249-5762 (Online) | ISSN : 2249-5770 (Print)

modal and harmonic-response analysis of two … · modal and harmonic-response analysis of two...

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