Translational Mechanical System old

# Translational Mechanical System old - Translational...

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School of Mechanical Engineering Purdue University ME375 Translation - 1 Translational Mechanical Systems Basic (Idealized) Modeling Elements Interconnection Relationships -Physical Laws Derive Equation of Motion (EOM) - SDOF Energy Transfer Series and Parallel Connections Derive Equation of Motion (EOM) - MDOF

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School of Mechanical Engineering Purdue University ME375 Translation - 2 Variables x : displacement [m] v : velocity [m/sec] a : acceleration [m/sec 2 ] f : force [N] p : power [Nm/sec] w : work ( energy ) [Nm] 1 [Nm] = 1 [J] (Joule) 1 0 1 0 2 2 1 0 0 ( ) ( ) ( ) ( ) ( ) t t t t d x x v dt d d d d v v x x x a dt dt dt dt d p f v f x w dt w t w t p t dt w t f x dt
School of Mechanical Engineering Purdue University ME375 Translation - 3 Idealized Modeling Elements Inertia (mass) Stiffness (spring) Dissipation (damper)

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School of Mechanical Engineering Purdue University ME375 Translation - 4 Spring Stiffness Element Idealization Massless No Damping Linear Stores Energy Basic (Idealized) Modeling Elements Reality 1/3 of the spring mass may be considered into the lumped model. In large displacement operation springs are nonlinear . x 2 K x 1 f S f S 2 1 S f K x x ( x 2 x 1 ) f S
School of Mechanical Engineering Purdue University ME375 Translation - 5 Practical Nonlinear Spring Engine Mount: #T062 VERTICAL -4000 -2000 0 2000 4000 -20 -15 -10 -5 0 5 DISP (mm) LOAD (N) x x K 2 force

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