TRC-SFD-1-07 - Tribology Group - Texas A&M University

2( ω−ω− )F = L x + F u ; L = K − M + i Cx xx d xx sxs xx s xx2( ω ω )y−−F = L y + F v ; L = K − M + i Cy yy d yy s s yy s yy(6)whereM = M + M + M; M = M + M + M;s−xx SFDxxf s−yy SFDyyfC = C + C ; C = C + C ;−s xx SFDxxsx s yy SFDyysy−(7)and ( x, y), ( F , F ) are the discrete Fourier Transform (DFT) of time varyingxydisplacements and forces, respectively. L xx , L yy are the linear transfer functions containingthe stiffness, inertia and damping coefficients. ( uv) , represent the DFT of the model2 2non-linear inputs ({ x, y} / x + yT ), obtained by building the velocity vector ( x, y) Tconstructed using the Fourier coefficients of the displacement (x c , x s ). This procedureeffectively reduces signal noise.The dry friction force (F d ) can be identified from Eq.(6) using two single frequencyforce excitations with different amplitude levels provided that the force coefficients in Eq.(7) are independent of the vibration amplitude. However, this is not the case for the SFDsince, as theory predicts and experimental results demonstrate [3], damping coefficientsare a function of the amplitude of journal motion. This dependency of the dampingcoefficient on the vibration amplitude is assumed to be linear for small differences isamplitudes, as shown in previous experimental work [3]. Thus, the squeeze film dampingforces are represented in the general form C SFDxx = a x x + b x and C SFDyy = a y y + b y , witha x,y and b x,y as generic constants. For multiple excitation load levels2( − )H = K − ω M + iωC + iω( a x + b ) + F Gi i ixx sxs xx sx x x d xx2( )y−i i iH = K − ω M + iωC + iω( a y + b ) + F G ; i=1... Nyy s s yy sy y y d yy(8)with19