TRC-SFD-1-06 - Tribology Group - Texas A&M University

VI.2 Parameter identification methodThis section describes the identification method employed to estimate the SFDparameters from centered circular orbit tests. The equations of motion for the test bearingsection are⎡M + Mf0 ⎤⎧&&x⎫⎡Ksx 0 ⎤⎧x⎫⎧Fx⎫ ⎧Fx⎫ ⎧Fx⎫⎢0 M M⎥⎨ ⎬+ ⎢f y 0 K⎥⎨ ⎬= ⎨ ⎬ −⎨ ⎬ −⎨ ⎬⎣ + ⎦⎩&&⎭ ⎣ sy⎦⎩y⎭⎩Fy⎭ ⎩Fy⎭ ⎩Fy⎭sealSFD(7)where M f =0.62 kg represents the estimated mass of fluid enclosed in the plenum abovethe fluid film land section and in the recirculation annulus. The SFD reaction forcesfollow the linearized description:⎧Fx⎫⎨ ⎬⎩Fy⎭SFD⎡C= ⎢⎣CSFD xxSFD yxCCSFD xySFD yy⎤⎥⎦⎧x&⎫⎨ ⎬⎩y&⎭⎡M+ ⎢⎣MSFD xxSFD yxMMSFD xySFD yy⎤ ⎧&&x⎫⎥ ⎨ ⎬⎦ ⎩&&y⎭(8)where { CSFD}αβ αβ=x,y , { MSFD}αβ αβ=x,y are the squeeze film damping and inertia forcecoefficients, respectively. The mechanical seal reaction force is expressed as⎧ x&⎫⎧Fx⎫ ⎪V⎪ ⎪⎧Csealx&x ⎪⎫⎨ ⎬ = Fμ⎨ ⎬ ≈ ⎨ ⎬⎩Fy⎭ y Cseal ⎪&⎪ ⎪ sealy&⎩ y ⎪⎭⎪⎩V⎪⎭(9)where V=( x& , y& ) T is the velocity vector and F μ is the dry-friction force and. C seal is anequivalent viscous damping coefficient that follows from equating the energy dissipatedby viscous forces to the energy dissipated from dry friction forces over one period ofmotion [20],C2∫ V dt = Edry= F ∫ V μsign(V dtF→μC seal= ;α=x,y(10)ω xseal)In the frequency domain the system can be represented asα37