10
IV
https://doi.org/10.22214/ijraset.2022.42073
April 2022
International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.538 Volume 10 Issue IV Apr 2022- Available at www.ijraset.com
Modal Analysis, Fatigue Analysis and Optimization of Tractor Drop Arm Using FEM Raviraj Inamke1, N. K. Nath2, R. R. Arakerimath3 1, 2, 3
Mechanical Department, JSPM’s RSCOE Tathwade, Pune
Abstract: The Drop Arm is part of the steering component in a Tractor. It is connected to the sector shaft and moves in angular motion with the help of the sector shaft. This motion causes the wheels to move left or right, depending on which way the steering wheel is moved. It is important you have your drop arm in good working condition because poor steering can be hazardous to you and those around you. A performance study will be carried to perform Failure, Fatigue & Modal Analysis of pitman arm using Ansys. The structural optimization will be done on the drop arm by changing the structure of pitman arm by modifying the geometry where stress values are critical. The meshing and boundary conditions will be applied and analysis will be carried out using Ansys 16.0. Keywords: Finite element analysis, Fatigue analysis, Modal analysis, Drop arm, FEM. I. INTRODUCTION This The Drop arm is a steering component that is used in an automobile or Tractor. It is a linkage between sector shaft of the steering box and drag link. It transmits the angular motion to the linear motion that is required to steer the wheels in desired direction. The arm is attached to the sector shaft and supports the drag link or centre link. It transmits the motion it receives from the steering box into the drag link, causing it to move Steering arm to turn the wheels in the appropriate direction. The track rod is attached between the opposite sides of the steering arms. A damaged or loose drop arm can cause inability to steer, wandering to the left or right while on the road, poor steering.
1) 2) 3) 4) 5)
II. OBJECTIVES To perform 3D Scanning of Drop Arm used in Tractor. To perform Failure analysis of Drop Arm. To analyse the fatigue life of the component. To perform Modal analysis of the component. Structural optimization for better design and increased efficiency.
III. METHODOLGY Phase I- Literature Survey Phase II- 3D Scanning & CAD Modelling Phase III- Failure, Fatigue & Modal Analysis of Drop Arm Phase IV- Optimization of Drop Arm Phase V- Failure, Fatigue and Modal Analysis of Optimized Drop Arm Phase VI- Validation and Report IV. LITERATURE SURVEY Pradeep B Patil et al. [1] Static and modal analysis results of existing pitman arm proved that the model is more stable and there is scope for optimization. The comparison, between modal analysis results of existing and optimized pitman arm has been performed and it is observed that the pitman arm is vibrationally stable. Sijith PM et al. [2] Performance study is carried out followed by static structural analysis and optimization to minimize the weight of the pitman arm and thereby reducing the material cost. Optimized model is then verified by physical testing. Vimal Rau Aparow et al. [3] has investigated 2 DOF mathematical models of Pitman arm steering system and derived using Newton’s law of motion and modelled in MATLAB/SIMULINK software. The performance of the electronically actuated Pitman arm steering system can be used to develop a firing-on-the-move actuator (FOMA) for an armoured vehicle. 1) 2) 3) 4) 5) 6)
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International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.538 Volume 10 Issue IV Apr 2022- Available at www.ijraset.com Srilekha Aurulla, G. and Gopala Krishna [4] has presented the static and modal analysis of steering lever link of a tractor to check its deformation, maximum stress and natural frequencies by using three materials. Aniket Kolekar et al. [5] has designed and fabricated the fixture which is used in the manufacturing of Pitman Arm of steering system. The fixture is designed by using software CATIAV5R21.The purpose of the fixture is to provide strength, holding, accuracy and interchangeability in the manufacturing of product. The main purpose of a fixture is to locate and, in the cases, hold a work piece during an operation. Shatabdee Sonawane et al. [6] Static analysis results of existing pitman arm proved that the model is more stable and there was scope for optimization The Pitman arm is optimized. The weight of original model is 974 gm and that of the optimized model is 840 gm. Weight of the component is reduced successfully up to 14% after optimization. The study confirmed that optimized pitman arm is structurally stable with good fatigue life. Pradeep B Patil et al. [7] Based on FEA it can be concluded that the optimized pitman arm has infinite life because it can withstand above 10,00,000 cycles. Weight reduction of 9.04 % is obtained without compromising the strength of pitman arm. Natural frequency of both conventional and optimized pitman arm is extracted. V.
3D SCANNING & CAD MODELLING
Fig. 1 3D Scanning Process
Fig. 2 3D Scanned Data
Fig. 3 3D Model Created from Scanned Data
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International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.538 Volume 10 Issue IV Apr 2022- Available at www.ijraset.com
Fig. 4 Real time Drop Arm Finite element analysis is a computational technique that is used in engineering to obtain approximate solutions of boundary value problems. The following are the steps for pre and post processing in FEM. 1) Define the geometry of the problem. 2) Discretise the model by meshing. 3) Define the element type(s) to be used. 4) Define the material properties of the elements. 5) Define the element connectivity. 6) Define the physical constraints (boundary conditions). 7) Define the loadings. 8) Solve the analytical problem. 9) Result evaluation. TABLE I MATERIAL PROPERTIES OF ALLOY STEEL Property Value Young’s modulus (E) 2.06 x 1011 Mpa Poisson’s ratio (v) 0.29 Density (ρ) 7.87 x 10-6 kg/mm3 Yield strength 450 Mpa VI. FORCE CALCULATIONS Total Mass of the vehicle, M1=Curb weight + Driver weight + Tractor Implement Weight = 1713 + 80 + 1000 = 2793 kg This weight is divided into front axle weight and rear axle weight. 35% of the total weight is taken by front axle and 65% is by rare axle. Therefore, Mass on the front axle, M2 = 977.55 kg Mass on one of the front wheels, M = 488.775 kg Width of tire, B = 132.08 mm Centre of rotation (king pin) to wheel, E = 145 mm Coefficient of friction, μ = 0.7 Distance from king pin centre to tie rod pin, L1 = 195 mm. T=Torque required to rotate one wheel (torque at king pin), T = M * g * µ * (B2/8) + E2 T = 511296.4938 N F = T/L1 F = 2622.0333 N Since single steering arm will be handling two wheels so the force on steering arm will be doubled. F = 5244.0666 N
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International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.538 Volume 10 Issue IV Apr 2022- Available at www.ijraset.com A. Stress Calculation σ = My/I σ = Maximum bending stress = Bending moment = Vertical distance away from the neutral axis = Moment of inertia y = b/2 y = 17 mm. I = (w * b3)/12 I = 63869 mm4. M=F*L M = 776121.8668 N-mm. TABLE III VIBRATION ANALYSIS (FREQUENCY CALCULATION) Mode Frequency 1st Mode
862.4
nd
1629.8
rd
3561.6
th
5018.2
th
5962.7
th
8393.6
2 Mode 3 Mode 4 Mode 5 Mode 6 Mode
B. Fatigue Life Calculation Sut = Ultimate tensile strength Sut = 450 Mpa = 45.887 kgf/mm2 Sa = Stress amplitude Sa = 0.8Sut = 360 Mpa = 36.709 kgf/mm2 Se = Endurance Se = 0.5Sut = 225 Mpa = 22.943 kgf/mm2 b = (-1/3) * log [(0.8*Sut)/Se] b = -0.067989 c = log [(0.8*Sut )2/Se] c = 1.768587 N = Number of life cycles before failure N = 10(-c/b) * Sa(1/b) = 0.994846 × 106 The existing pitman arm will fail after 0.994846 × 106cycles. We say that component is having infinite life if it exceeds one lakh cycles. VII. FINITE ELEMENT ANALYSIS OF DROP ARM For analysis, one end of the pitman arm (larger side connected to sector shaft) is rigidly fixed and on another end, load is applied i.e., of 5244.0666 N. 1) Mesh Details: Nodes: 215655, Elements: 143218
Fig. 5 Meshed Model
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International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.538 Volume 10 Issue IV Apr 2022- Available at www.ijraset.com 2) Deformation Plot: Maximum Deformation is 0.63854 mm.
Fig. 6 Deformation Plot 3) Stress Plot
Fig. 7 Equivalent (von-Mises) Stress Maximum Stress: 205.7 MPa Minimum Stress: 0.0056274 MPa Ultimate Strength: 450 MPa Maximum Force component can withstand: 11472.026 N As stress is well within the limit and deformation is less hence there is scope for optimization. VIII.
FATIGUE ANALYSIS OF DROP ARM
Fig. 8 Fatigue Life of Drop Arm
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International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.538 Volume 10 Issue IV Apr 2022- Available at www.ijraset.com Minimum Fatigue Life (Cycles): 23122, Maximum Fatigue Life (Cycles): 1×106
Fig. 9 Damage of Drop Arm Minimum Damage: 1000, Maximum Damage: 43248 IX. MODAL ANALYSIS OF DROP ARM Modal frequency results of 6 modes of drop arm calculated in Ansys 16.0 are as below. TABLE IIIII MODAL ANALYSIS OF DROP ARM Modal Frequency Drop Arm 1st Mode
896.86
2nd Mode
1560
3rd Mode
3617.4
4th Mode
5047.1
5th Mode
6004.2
6th Mode
8284.4
X. OPTIMIZATION OF DROP ARM A. Structural Optimization The optimization of drop arm is done by modifying the geometry of drop arm where stress concentration is highest and lowest. Drop arm is optimized by modifying stress concentration areas and improving geometry for better stress distribution. Extra material is added on top side of drop arm to provide better stress distribution in z direction and extreme edges are smoothened. A slot is also added in low stress areas to compensate for increased weight and netter stiffness in Y direction. The optimized geometry as below.
Fig. 10 Optimized Drop Arm
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International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.538 Volume 10 Issue IV Apr 2022- Available at www.ijraset.com B. Material Optimization New Material selected for optimization of Drop arm is AISI 4304 - EN24T. Material properties of EN24T are as belowTABLE IVV MATERIAL PROPERTIES OF EN24T Properties
Metric
English
7.85 g/cc
0.284 lb/in³
Hardness, Brinell
363
363
Hardness, Knoop
392
392
Hardness, Rockwell B
100
100
Hardness, Rockwell C
40
40
Hardness, Vickers
384
384
Tensile Strength, Ultimate
1282 MPa
185900 psi
Tensile Strength, Yield
862 MPa
125000 psi
Modulus of Elasticity
200 GPa
29000 ksi
Bulk Modulus
159 GPa
23100 ksi
Poissons Ratio
0.29
0.29
Shear Modulus
78.0 GPa
11300 ksi
Density
C. Deformation Plot
Fig. 11 Deformation Plot of Optimized Drop Arm Maximum Deformation is 0.62685 mm.
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International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.538 Volume 10 Issue IV Apr 2022- Available at www.ijraset.com D. Stress Plot
Fig. 12 Equivalent (von-Mises) Stress Maximum Stress: 185.58 MPa Minimum Stress: 0.0045697 MPa Ultimate Strength: 862 MPa Maximum Force component can withstand: 24357.64 N XI. FATIGUE ANALYSIS OF OPTIMIZED DROP ARM A. Results for Fatigue Analysis Force Applied: 5244.0666 N Minimum Fatigue Life (Cycles): 33730 Maximum Fatigue Life (Cycles): 1×106
Fig. 13 Fatigue Life of Optimized Drop Arm
Fig. 14 Damage of Optimized Drop Arm Minimum Damage: 1000, Maximum Damage: 29647
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International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.538 Volume 10 Issue IV Apr 2022- Available at www.ijraset.com XII. MODAL ANALYSIS OF OPTIMIZED DROP ARM The Modal frequency results of 6 modes of Optimized drop arm calculated in Ansys 16.0 are as below. TABLE V MODAL ANALYSIS OF OPTIMIZED DROP ARM Modal Frequency Optimized Drop Arm 1st Mode
890.3
2nd Mode
1553.8
3rd Mode
3711
4th Mode
4437.4
5th Mode
6147.1
6th Mode
8446.3
XIII.
RESULTS AND DISCUSSIONS
A. Fatigue Analysis
Parameter Fatigue Life (Cycles) Damage
TABLE VI COMPARISON OF FATIGUE LIFE Optimized Drop Drop Arm Arm Min Max Min Max 23122
1×106
33730
1×106
1000
43248
1000
29647
B. Structural Analysis TABLE VII COMPARISON OF STRUCTURAL ANALYSIS RESULTS Parameter
Drop Arm
Optimized Drop Arm
Min
Max
Min
Max
0.0056274
205.7
0.0045697
185.58
8
0.0011
3.5763 ×10-8
0.0009279
Ultimate Strength (Mpa)
-
450
-
862
Maximum Force component can withstand(N)
-
11472.03
-
24357.64
Maximum Deformation (mm)
0
0.63854
0
0.62685
Equivalent (von Mises) Stress (Mpa) Equivalent Elastic Strain (mm/mm)
4.0917×10-
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International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.538 Volume 10 Issue IV Apr 2022- Available at www.ijraset.com C. Modal Analysis TABLE VIII COMPARISON OF MODAL ANALYSIS RESULTS Modal Frequency Drop Arm Optimized Drop Arm 1st Mode
896.86
890.3
nd
1560
1553.8
rd
3617.4
3711
th
5047.1
4437.4
th
6004.2
6147.1
th
8284.4
8446.3
2 Mode 3 Mode 4 Mode 5 Mode 6 Mode
XIV. CONCLUSION 1) Static and modal analysis results of existing pitman arm proved that there is scope for optimization. 2) Von Mises stress in optimized drop arm is reduced by 9.78%, Maximum force drop arm can withstand is increased by 112% and deformation is reduced by 2% under same loading conditions. 3) The comparison, between fatigue life results of existing and optimized pitman arm has been performed and it is observed that the pitman arm is having infinite life. 4) The comparison, between modal analysis results of existing and optimized pitman arm has been performed and it is observed that the pitman arm is vibrationally stable. The above steady confirmed the optimized pitman arm is vibrationally and structurally stable with good fatigue life. REFERENCES [1] [2] [3]
[4] [5] [6] [7]
Pradeep B Patil and P D Darade “Modal Analysis, Fatigue Analysis and Optimization of Pitman Arm Using FEM.” International Journal of Research and Scientific Innovation (IJRSI), Volume V, Issue IX, September 2018, ISSN 2321–2705. Sijith PM, Prof. Shashank Gawade, Prof. S.S Kelkar “CAE Analysis and Structural Optimization of Pitman Arm” International Journal of Science, Engineering and Technology Research (IJSETR), Vol. 5, Issue 6, June2016, ISSN: 2278-7798, pp.1901-1903. Vimal Rau Aparow, KhisbullahHudha, ZulkiffliAbdKadir, Megat Mohamad HamdanMegat Ahmad, and Shohaimi Abdullah “Modeling, Validation, and Control of ElectronicallyActuated Pitman Arm Steering for Armored Vehicle” International Journal of Vehicular Technology, Volume 2016, Article ID 2175204, pp. 1-12 Srilekha Aurulla , G. Gopala Krishna “Modeling and Analysis of Steering Lever Link of a Tractor” IJIRSET Vol. 5, Issue 11, November 2016, pp. 1980119808 Aniket Kolekar, Mr. Shubham R. Gound, Mr. Mahesh S. Ban “Design of Fixture for Manufacturing of Pitman Arm” IRJET, Volume: 04, Issue: 05 May -2017, pp. 1714-1720 Shatabdee Sonawane, Prof. P. M. Sonawane "Structural Analysis and Optimization of Pitman ARM", International Journal of Engineering Research & Technology (IJERT), ISSN: 2278-0181, Vol. 9 Issue 08, August-2020. Pradeep B Patil and P D Darade “Vibrational Analysis, Life Prediction and Optimization of Pitman Arm Using FEM.” International Journal of Computational Engineering Research (IJCER), vol. 08, no. 05, 2018, pp. 18-23.
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