Nenshi Patel_2021ume1411[1]-1 4 (2).pptx

A presentation on training

1. Design Optimization and Stiffness Estimation of a Swingarm using FEM & MATLAB MES- 417 Industrial Training Seminar Presented By : Nenshi Patel 2021ume1411 M4 MNIT Jaipur Guided By : Mr. Sivanesa s elvam Thangarajan, Manager -R&D (EV & Technology), Mr. S P Senthil Nathan, Deputy Manager-R&D, TVS Motor, Hosur, Tamil Nadu. Presented To: Dr. G. D. Agarwal Professor, Mechanical Engineering Dr. Jinesh Jain Associate Professor, Mechanical Engineering MNIT Jaipur Duration: 22nd May 2024 – 19th July 2024 1

2. Contents:   About TVS Motor Project  What is a Swingarm?   Approach Methodology Fine Element Method (FEM) Results 2

3. About TVS Motor T. V. Sundram Iyengar (Founder of TVS Motor) TVS Motor Company  is a reputed two and three-wheeler manufacturer globally, an Indian Multinational. Head-Quarter : Chennai, Tamil Nadu Manufacturing Facilities : Hosur, Tamil Nadu Mysore, Karnataka Nalagarh, Himachal Karawang, Indonesia Founder : T. V. Sundram Iyengar CEO : K N Radhakrishnan Slogan : “ Inspiration in Motion”. TVS Motor Company is the third largest 2-wheeler company in India in terms of revenue and second largest two wheeler exporter in India. 3

4. Project Objective : The aim of this project is to develop a mathematical model to determine the Stiffness of a preliminary design of a Swingarm using MATLAB. WHY Needed?? Stiffness estimation & design optimization requires a significant amount of time and effort from both designers and FEM simulators being an iterative process. Hence, by developing a mathematical model it will help to reduce the lead time. 4

5. What is a Swingarm? It is a part of the rear suspension system. Mechanical device which attaches the rear wheel to body/frame. Allows the rear wheel to pivot vertically, to absorb shocks and vibrations over the bumps. 5 Mono-Suspension Swingarm (only one shock absorber) Shock-absorber Pivot point

6. Functions & Design Considerations 6 Provides support and stability to the vehicle’s body. Acts as a shock absorber. Allows the rear wheel to move independently up and down thereby not loosing contact with the road. Distributes the stresses and forces exerted on the rear wheel uniformly Strength & Durability Stiffness & Flexibility Lightweight Design

7. Approach 7 Since we know the swingarm is a component that absorbs vibrations, hence it is evident that it should have a tendency to return back to its original form after being subjected to loads. In design, the parameter measuring such a tendency is known as stiffness . Component undergoing vibration experiences deflection, which is directly proportional to the Force applied. Hence, where, ‘k’ is the stiffness of the element.  

8. Types Of Stiffness 8 Axial stiffness   Torsional stiffness   Bending stiffness :   Resistance to deformation along the length of the object. Resistance to bending or flexural deformation. Resistance to twisting or rotational deformation. Where, A = Cross sectional area E = Young's modulus L = Length of Element G = Shear Modulus I = Moment of inertia J = Polar moment of inertia

9. Methodology 9 Fig : 1 Preliminary design of a swingarm For a particular bike, there might be some dimension requirements, through the analysis of the designer. This dimension can be treated as the initial guess. The preliminary design of the swing arm can be considered as in Fig. 1 Using the model, the stiffness corresponding to it can be estimated. The swingarm is symmetrical about longitudinal plane Hence node 1=4, 2=5, 3=6 . In order to calculate the stiffness we go for Fine Element Method (FEM). Frame Wheel

10. Fine Element Method (FEM) (Stiffness Matrix Method) 10 Fine element method is a numerical technique which is used to find the approximate solutions of complex problems in engineering. It breaks the larger problem into smaller one. To develop the mathematical model we use the FEM. Steps are as follows : Fig: 1 is divided into 7 nodes and 6 elements. Determining the Element Stiffness Matrix for each element. Calculating the Global Stiffness Matrix. Applying the boundary conditions. Solving the system of equations. Calculating the stiffness at the most critical point. Fig : 1

11. 11 We know that [ F ] = [ U ] [ k ] Calculation of Element Stiffness Matrix for each element by the formula: Where, A : Cross-section area ( assumed to be constant throughout). E : Young’s Modulus. L : Length of the element. [ k ] is the local stiffness matrix [ U ] is the deflection matrix [ F ] is the force matrix

12. 12 Element             Where, N : Axial force Q : Transverse force M : Moment u : Axial deformation v : Lateral deformation Ɵ : Angular deformation Since, [ F ] = [ U ] [ k ] The Local Stiffness matrix for each element is calculate this way, for this case stiffness matrix ranges from k1 to k3 Each node will have 3 degree of freedom (dof). Therefore element matrix is of order 6×6

13. 13 Global stiffness matrix calculation : 12×12 Matrix Since we are considering only the left half of the swingarm.

14. Boundary Conditions 14 Fixed to the Frame Point 1 and 4 are directly connected to the frame, and are considered to be fixed supports. T here is no movement in the direction the motorbike moves. Load is applied at point 3 and 6 specific to the type of motion the vehicle is undergoing: 1. Weight distribution: weight of th e vehicle that is weight of two-wheeler + wight of rider(s). 2. Lateral load is acted upon the swingarm while cornering.

15. 15 4. T here While calculating torsional stiffness, element across nodes 2,7,5 undergoes twist, hence a torque at node 2 or 5 Central member undergoing rotational deformation

16. 16 In this case there is torsional stiffness acts at node 2 and 5 hence Element stiffness matrix changes as follows: Where, G : Shear Modulus J : Polar moment of inertia Swingarm under Torsion

17. 17 1. Weight distribution case 2. Cornering case Lateral stiffness =   Vertical stiffness =   Torsional stiffness =   Loading Conditions

18. 18 By solving these system of equations one can find the deflection at the required points. Final Global Stiffness Matrix U7 = 0 V7 = 0 Θ7 = 0 7 7 7 N7 Q7 M7

19. 19 MATLAB Code

20. 20

21. 21 F or dimensions : L1 = 163.7 mm L2 = 366.4 mm L3 = 117.5 mm and Material is Steel i.e ., E = 210 Gpa, G= 79 GPa Length1(mm) Length2(mm) Mid length(mm) Deflection(mm) Load(N) Lateral Stiffness(N/mm) Software Error% 163.7 530.1 117.5 0.0021 1 463.4638 458.274 1.11 Length1(mm) Length2(mm) Mid length(mm) Deflection(mm) Load(N) Vertical Stiffness(N/mm) Software Error% 163.7 530.1 117.5 1.665 588.6 353.4673 353.5 0.01 Length1(mm) Length2(mm) Mid length(mm Deflection(mm) Load(N) Torsional Stiffness(Nmm/deg) Software Error% 163.7 530.1 117.5 0.589 588.6 240597 197289.54 18 Results-1 (For Rectangular cross-section)

22. 22 Results-2 (For Circular cross-section) F or dimensions : L1 = 163.7 mm L2 = 366.4 mm L3 = 117.5 mm and Material is Steel i.e ., E = 210 Gpa, G= 79 GPa Length1(mm) Length2(mm) Mid length(mm) Deflection(mm) Load(N) Lateral Stiffness(N/mm) 163.7 530.1 117.5 0.0021 1 472.905 Length1(mm) Length2(mm) Mid length(mm) Deflection(mm) Load(N) Vertical Stiffness(N/mm) 163.7 530.1 117.5 1.5803 588.6 372.440 Length1(mm) Length2(mm) Mid length(mm Deflection(mm) Load(N) Torsional Stiffness(Nmm/deg) 163.7 530.1 117.5 0.5591 588.6 253657.211

23. 23 Now, going a step forward we i ncreasing the number of nodes and blend the cross-sectional areas that are not constant. There are no more sudden change in dimension, hence better stiffness may be expected. The same algorithm can be applied to it as well but with increased nodes Variable cross-sectional area (here the previous assumption isn’t valid) Raider Swingarm (CAD Model) Taking a step ahead

24. 24 Vehicle Dynamics, Vittore Cossalter. Optimization Of Deflection Equation For Tapered Cantilever Beams using the Finite Element Method. An Introduction to The Finite Element Method, by J. N. REDDY. Static structural analysis of a motorcycle’s single sided swingarm, by Rui Miguel Costa Dias. Design and Structural Analysis of a Front Single-Sided Swingarm for an Electric Three- Wheel Motorcycle. References

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26. 26 Thankyou