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Unformatted text preview: Mechanical System System with linear motion Example : Vehicle (train) driven by a linear motor vehicle f linear motor u e f L Fig. 1 Equivalent system mass (M) friction (D) speed (u) f dr f M f L f fr Fig. 2 Equilibrium equation of mechanical system ( called also force equation, or motion equation ) : dr M fr L f f f f = + + (1) where: f dr driving force (electromagnetic force developed by the linear motor), f M inertia force, which opposes the acceleration a of mass M M f M a = (2) f fr friction force 1 fr F D u = (3) in which D is a friction coefficient and u is speed f L load force (attached to the vehicle) Quantities of a mechanical system speed: dx d u x dt dt = = (4) position: ( 29 (0) dx x t x dt dt = + (5) acceleration: 2 2 du d x a dt dt = = (6) In Laplace domain: ( 29 u s s x = , ( 29 2 a s s u s x = = (7) where: d s dt = , and 2 2 2 d s dt = (8) inertia force: M dr L fr f f f f M a = = (9) From Eqns. 6 and 8: Speed ( 29 dr L f f u s M s D = + (10) Position ( 29 1 (0) x s x u s = + (11) differential work: dW f dx = (12) 2 power: ( ) dW dx p t f dt dt = = (13) input power: in dr M L fr P f u f u f u f u = = + + (14) kinetic energy: 2 1 2 M W Mu = (15) Block Diagram of the mechanical system Blocks (with the equations they represent): + _ f fr f dr f L f + M...
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 Fall '06
 Scalzo

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