Modeling of Mechanical (Lumped Parameter) Elements

Equivalent Damping Coefficients:Select an equivalent velocity and equate the dissipated powersP = F X= DVDd2(a) dampers connected by leversP D = {D 1 V 2 1 + D 2 V 2 2} = D eq V eq 2[N.m=J]ω = θLet V eq = V 1 & since V 2 = ωL 2 , V 1 = ωL 1then V 2 = V 1 (L 2 / L 1 ) andD eq = D 1 + D 2 (L 2 / L 1 ) 2 [Ns/m](b) torsional dampers on geared shafts θ N = θ N , where N is the number of teethSince1 1 2 2and selecting θeq= θ , then1D eq = D 1 + D 2 (N 1 / N 2 ) 2[N.m.s/rad](c) coupled torsional and translationaldampersLet ω= θ , V eq = V & since V = ω R, thenD eq = D + D t / R 2Or let θeq= θ[N.s/m]1 then the equivalent torsional damper isD eq = D R 2 + D t[N.m.s/rad]Note: in (a) thru (c) one of the dashpot ends is connected to ground.MEEN 617 Notes: Handout 1 / © Luis San Andrés 2008 1.16