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Gear rattle is an annoying noise phenomena of the automotive transmission, which is mainly induced by torsional fluctuation of engine. In this study, torsional vibration of 3 cylinder powertrain is analyzed and improved for reducing the gear rattle from transmission by using parametric optimization. One dimensional Multi-body mathematical model for the torsional vibrations of front wheel drive automotive drivetrain is developed and utilized for the optimization of sensitive parameters of the driveline. Second order differential equations of the mathematical model are solved by using MATLAB and the output response is validated with the test data. Parametric optimization is conducted by using design of experiment method. The updated model is further utilized for optimizing the flywheel inertia, driveshaft stiffness and clutch stiffness. Mathematical modelling and optimization process has helped to achieve NVH targets for driveline.