# Modal Analysis, Fatigue Analysis and Optimization of Drop ARM using FEM

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#### Modal Analysis, Fatigue Analysis and Optimization of Drop ARM using FEM

Raviraj Inamke

PG Student, Department of Mechanical Engineering JSPMs Rajarshi Shahu College of Engineering, Tathawade, Pune, Maharashtra, India.

Dr. N. K. Nath

Professor, Department of Mechanical Engineering JSPMs Rajarshi Shahu College of Engineering,

Dr. R.R. Arakerimath

HOD, Department of Mechanical Engineering JSPMs Rajarshi Shahu College of Engineering, Tathawade, Pune, Maharashtra, India

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.

1. INTRODUCTION

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 center 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.

2. OBJECTIVES

• To perform 3D Scanning of Drop Arm used in Tractor.

• To perform Failure analysis of Drop Arm.

• To analyze the fatigue life of the component.

• To perform Modal analysis of the component.

• Structural optimization for better design and increased efficiency.

3. METHOD OLGY 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

4. 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 Newtons law of motion and modeled 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 armored vehicle.

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 upto 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.

5. 3D SCANNING & CAD MODELLING

Fig. 1. 3D Scanning Process

Fig. 2. 3D Scanning Equipment

Fig. 3. 3D Scanned Data

Fig. 4. 3D Model Created from

Scanned Data

Fig. 5. 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. Discretize 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).

8. Solve the analytical problem.

9. Result evaluation.

 Property Value Youngs modulus (E) 2.06 x 1011 Mpa Poissons ratio (v) 0.29 Density () 7.87 x 10-6 kg/mm3 Yield strength 450 Mpa
 Property Value Youngs modulus (E) 2.06 x 1011 Mpa Poissons ratio (v) 0.29 Density () 7.87 x 10-6 kg/mm3 Yield strength 450 Mpa

M = F * L (6)

M = 776121.8668 N-mm.

TABLE I. Material properties of Alloy Steel

6. FORCE CALCULATIONS Total Mass of the vehicle,

M1=Curb weight + Driver weight + Tractor Implement Weight

M1= 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, = 0.7

Distance from king pin center to tie rod pin, L1 = 195 mm.

T=Torque required to rotate one wheel (torque at king pin),

T = M * g * Âµ * (B2/8) + E2 (1) T = 511296.4938 N

F = T/L1 (2) F = 2622.0333 N

Since single steering arm will be handing two wheels so the force on steering arm will be doubled.

F = 5244.0666 N

Stress calculation:

= My/I (3)

= Maximum bending stress

= Bending moment

= Vertical distance away from the neutral axis

= Moment of inertia

y = b/2 (4) y = 17 mm.

I = (w * b3)/12 (5) I = 63869 mm4.

The maximum bending stress,

= My/I (7) = 206.58021 Mpa.

Vibration analysis (frequency calculation):

For natural frequency,

n = k2 [EI/(AL4 )]1/2 * (1/2) (8) Where,

k = (2n-1) * (/2) (9)

 Mode Frequency 1st Mode 862.4 2nd Mode 1629.8 3rd Mode 3561.6 4th Mode 5018.2 5th Mode 5962.7 6th Mode 8393.6

TABLE II. Vibration analysis (frequency calculation)

Fatigue life calculation:

N = 10(-c/b) * Sa(1/b) (10)

b = (-1/3) * log [(0.8*Sut)/Se] (11)

c = log [(0.8*Sut )2/Se] (12)

N = Number of life cycles before failure Sut = Ultimate tensile strength

Sa = Stress amplitude Se = Endurance

Sut = 450 Mpa = 45.887 kgf/mm2

Sa = 0.8Sut = 360 Mpa = 36.709 kgf/mm2 Se = 0.5Sut = 225 Mpa = 22.943 kgf/mm2 b = -0.067989

c = 1.768587

N = 0.994846 Ã— 106

The existing pitman arm will fail after 0.994846 Ã— 106cycles. We say that component is having infinite life if it exceeds one

lakh cycles.

7. 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.

Fig. 6. Meshed Model

Mesh Details:

Nodes: 215655

Elements: 143218

Deformation Plot:

Fig. 7. Deformation Plot

Maximum Deformation is 0.63854 mm.

Stress plot:

Fig. 8. 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.

8. FATIGUE ANALYSIS OF DROP ARM

Results for fatigue analysis:

Force Applied: 5244.0666 N

Fig. 9. Fatigue Life of Drop Arm Minimum Fatigue Life (Cycles): 23122 Maximum Fatigue Life (Cycles): 1Ã—106

Fig. 10. Damage of Drop Arm

Minimum Damage: 1000

Maximum Damage: 43248

9. MODAL ANALYSIS OF DROP ARM

Modal frequency results of 6 modes of drop arm calculated in Ansys 16.0 are as below.

 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

TABLE III. Modal Analysis of Drop Arm

10. OPTIMIZATION OF DROP ARM

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. 11. Optimized Drop Arm

Deformation Plot:

Fig. 12. Deformation Plot of Optimized

Drop Arm

Maximum Deformation is 0.60859 mm.

Stress plot:

Fig. 13. Equivalent (von-Mises) Stress

Maximum Stress: 185.24 MPa Minimum Stress: 0.00054878 MPa Ultimate Strength: 450 MPa

Maximum Force component can withstand: 12738.886 N

11. FATIGUE ANALYSIS OF OPTIMIZED DROP ARM

Results for fatigue analysis:

Force Applied: 5244.0666 N

Minimum Fatigue Life (Cycles): 33957 Maximum Fatigue Life (Cycles): 1Ã—106

Fig. 14. Fatigue Life of Optimized Drop

Arm

Fig. 15. Damage of Optimized Drop Arm

Minimum Damage: 1000

Maximum Damage: 29449

12. 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.

 Modal Frequency Optimized Drop Arm 1st Mode 902.39 2nd Mode 1574.9 3rd Mode 3761.5 4th Mode 4497.9 5th Mode 6230.7 6th Mode 8561.1

TABLE IV. Modal Analysis of Optimized Drop Arm

13. RESULTS AND DISCUSSIONS

Fatigue Analysis:

 Parameter Drop Arm Optimized Drop Arm Min Max Min Max Fatigue Life (Cycles) 23122 1Ã—106 33957 1Ã—106 Damage 1000 43248 1000 29449

TABLE V. Comparison of Fatigue life

Structural Analysis:

 Parameter Drop Arm Optimized Drop Arm Min Max Min Max Equivalent (von-Mises) Stress (Mpa) 0.0056274 205.7 0.0054878 185.24 Equivalent Elastic Strain (mm/mm) 4.0917Ã—10-8 0.0011 4.1071Ã—10-8 0.0008992 Ultimate Strength (Mpa) – 450 – 450 Maximum Force component can withstand(N) – 11472.03 – 12738.886 Maximum Deformation (mm) 0 0.63854 0 0.60859

TABLE VI. Comparison of structural analysis results

Modal Analysis:

 Modal Frequency Drop Arm Optimized Drop Arm 1st Mode 896.86 902.39 2nd Mode 1560 1574.9 3rd Mode 3617.4 3761.5 4th Mode 5047.1 4497.9 5th Mode 6004.2 6230.7 6th Mode 8284.4 8561.1

TABLE VII. Comparison of Modal Analysis Results

14. CONCLUSION

• Static and modal analysis results of existing pitman arm proved that there is scope for optimization.

• Von-Mises stress in optimized drop arm is reduced by 10%, Maximum force drop arm can withstand is increased by 11% and deformation is reduced by 5% under same loading conditions.

• 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.

• The comparison, between modal analysis results of existing and optimzed 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. 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 23212705.

2. 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.

3. 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

4. Srilekha Aurulla , G. Gopala Krishna Modeling and Analysis of Steering Lever Link of a Tractor IJIRSET Vol. 5, Issue 11,

November 2016, pp. 19801-19808

5. 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

6. 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.

7. 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.