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

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,

Tathawade, Pune, Maharashtra, India.

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).

   7. Define the loadings.

   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 * µ * (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 × 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.

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): 1×106

   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): 1×106

    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	1×106	33957	1×106
    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)	4.0917×10-8	0.0011	4.1071×10-8	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.