OPTIMAL DESIGN OF CLUTCH FRICTION PAD MAE 598: DESIGN OPTIMIZATION OPTIMAL DESIGN OF CLUTCH FRICTION PAD Presented by: VELUGUBANTLA SRINIVASA MURALIKRISHNA ADARSH VENKITESWARAN VARUN SUBRAMONIAM

PARAMETRIC OPTIMIZATION OF A CLUTCH SYSTEM Problem statement Design a rigid drive clutch system that meets multiple objectives such as Vibrational rigidity, Structural and Thermal strength. To demonstrate a systematic approach to solving multi-objective problems by approximating multiple Pareto optimal solutions by Response Surface Optimization. Courtesy: google images Modal Analysis1 Structural Analysis2 Thermal Analysis3 Minimize Temperature Maximize Natural Frequency Minimize Equivalent Stress 1 Velugubantla Srinivasa MuraliKrishna, 2 Adarsh, 3 Varun

SUB-SYSTEM OPTMIZATION METHODOLOGY Parameter set Constraint set g1: 140 ≤ P1 ≤ 160 g2 : 2 ≤ P2 ≤ 10 g3: 0.5 ≤ P3 ≤ 3.5 Friction Lining Parameter set P1- Inner Dia P2- Pad thk P3 – Pad Facing thk P1 P2 P3 Parametric Model Modal Analysis Structural Analysis Thermal Analysis Design Of Experiments Latin Hyper Cube Sampling Metamodeling Standard Response surface-(Full 2nd order polynomial) Response Surface Optimization Non Linear Programming by Quadratic Lagrangian Method (NLPQL) Maximize Natural Frequency Minimize Equivalent Stress Temperature

MODAL ANALYSIS Objective Maximize the natural frequency of clutch assembly f = (P1,P2,P3) to avoid resonance with Engine and Transmission systems Influence of parameter values Initial design Robustness of solution (Goodness of fit) Final optimized design 31.5 % improvement Parameter Starting Point Final Design P1 (mm) 160 140 (active) P2 (mm) 2.7 2 (active) P3 (mm) 0.8 0.5 (active) Output Initial Value Optimized Value Simulated Value Frequency (hz) 42 54.2 55.26

STRUCTURAL ANALYSIS Objective Minimize the equivalent stress acting on the friction pad σeq = (P1,P2,P3) to avoid failure during dynamic loading Influence of parameter values Initial design Robustness of solution (Goodness of fit) Final optimized design 27.16 % improvement Parameter Starting Point Final Design P1 (mm) 160 160 (active) P2 (mm) 2.7 10 (active) P3 (mm) 0.8 2.52 Output Initial Value Optimized Value Simulated Value Stress(MPa) 0.254 0.18 0.185

THERMAL ANALYSIS Objective Minimize the temperature generated on the friction pad T= (P1,P2,P3) Influence of parameter values Initial design Final optimized design Robustness of solution (Goodness of fit) 31.3 % improvement Parameter Starting Point Final Design P1 (mm) 160 150 P2 (mm) 2.7 6 P3 (mm) 0.8 3.5 (active) Output Initial Value Optimized Value Simulated Value Temperature(ᵒC) 109.9 76.79 75.46

COMPLETE SYSTEM OPTMIZATION METHODOLOGY Multi objective Genetic Algorithm Method(MOGA) Single Objective optimization (Other two objectives are constraints) Non Linear Programming by Quadratic Lagrangian Method (NLPQL) Pareto Optimal Surface Pareto Optimal Surface

RESULTS COMPARISON (Pareto Surface) Multi-objective (MOGA) Single-objective (NLPQL) MOGA Algorithm Hybrid variant of popular NSGA-II ( Non- dominant Sorted Genetic Algorithm) Used for continuous problems Constraint handling using same non-dominance principle. Hence, no penalty functions and Lagrange multipliers needed NLPQL Algorithm Generates a sequence of QP sub-problems obtained by quadratic approx. of Lagrangian function and Linearization of constraints. Second order information is updated by Quasi-Newton formula method and stabilized by an Armijo line search

Lessons Learnt System based optimization Different methods used for sampling in DOE Comparison of various Optimization Algorithms Response Surface metamodeling. Active constraint identification and monotonicity Pareto Surface and regression analysis