Walter D’Ambrogio and Annalisa Fregolent As outlined in Fig. 3, the unknown subsystemA is a 2-DoFs system made by the output shaft to which gear 7 and flywheel 8 are locked. Note that gear 6 is not locked to the output shaft so that it can be considered as belonging to the residual subsystemB. For the residual subsystemB, rotations θB 1 ··· θB 6 can be expressed through a reduced set of four independent rotations, as shown by Eq. (40): ⎧⎪ ⎪⎪⎨ ⎪⎪⎪⎪⎩ θB 1 θB 2 θB 3 θB 4 θB 5 θB 6 ⎫⎪ ⎪⎪⎬ ⎪⎪⎪⎪⎭ = ⎡ ⎢⎢⎢ ⎢⎢⎢ ⎣ 1 0 0 0 0 z3/z2 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 z4/z6 0 ⎤ ⎥⎥⎥ ⎥⎥⎥ ⎦ ⎧⎪ ⎨ ⎪⎩ θB 1 θB 3 θB 4 θB 5 ⎫⎪ ⎬ ⎪⎭ (40) Therefore, subsystemBcan be modelled as a 4 DoFs lumped parameter system. To have an idea of the dynamic behaviour of the torsional system, the natural frequencies of the subsystems Aand B, and of the coupled systemABare shown in Table 2. Table 2 Natural frequencies of the systems [Hz] Mode System 1 2 3 4 5 A 26.3881 72.2981 – – – B 22.7742 56.3484 120.4927 416.6248 – AB 23.3477 37.5007 59.7304 106.7501 184.4634 4.1 Decoupling It is assumed that the rotational FRFs (mobilities) describing the angular velocity/torque relationship of the coupled systemAB, and the mechanical impedance of the residual subsystemBare known. It is desired to determine the rotational mobility of subsystemA. The exact FRFs ˆHi j of the coupled systemABand the impedances of subsystemB are computed starting from the physical parameters shown in Table 1. To simulate the effect of noise on the FRFs of the coupled system, a complex random perturbation is added to the true FRFs: Hi j(ωk)= ˆHi j(ωk)+mi j,k +ini j,k (41) where mi j,k and ni j,k are independent random variables with gaussian distribution, zero mean and a standard deviation of 0.1 rad/sNm. The effect of such perturbation 62
RkJQdWJsaXNoZXIy MTMzNzEzMQ==