Large deformation gear model

By using the lumped parameter method, a 12 degree of freedom dynamic model of a pair of fixed axis gears is established, in which the meshing excitation, support conditions, drive and load of the gear pair are comprehensively considered

Where, q = [q1q2] t is the generalized displacement vector of gear pair, where IQ (I = 1, 2) is the generalized displacement of driving and driven gears respectively; m = blkdiag (M1, M2) is the mass matrix of gear pair, where Mi = diag (MI, MI, MI, II, IX) (II = 1, 2), MI is the mass of gear I, IIx is the moment of inertia of gear I around X axis, Blkdiag () and Diag () are MATLAB Function, representing block diagonal matrix and diagonal matrix respectively; KB is the stiffness matrix of bearing, generally using diagonal matrix, each element on diagonal represents the support stiffness of bearing in corresponding displacement direction; if nonlinear bearing model is adopted, KB becomes zero matrix, and the corresponding bearing support reaction component is added to the right of equal sign of equation; CB is the damping matrix of bearing, using proportional matrix Damping formula CB = AMB + β MB, where MB is the zero matrix; RM is the meshing excitation vector of gear pair, RM = [f1t1f2t2] t, FI and Ti (I = 1 and 2) are calculated by formula respectively; re is the external load vector of gear pair, including drive and load.