Issue34

R. Citarella et alii, Frattura ed Integrità Strutturale, 34 (2015) 554-563; DOI: 10.3221/IGF-ESIS.34.61 557 Applying these formulas for the two considered couplings, the levels of the noise factors i 1 and i 2 were obtained, assuming that they are separated from each other by 2  and are equidistant from the mean: 1. interference fit H7/n6 (i max =39  m; i min = -10  m; i med =  i =14.5  m;  i =5.9  m): i 11 =  i  +  i =20.4  m; i 12 =  i  -  i =8.6  m; 2. interference fit H7/p6 (i max =51  m; i min =2  m; i med =  i =26.5  m;  i =5.9  m): i 21 =  i  +  i = 32.4  m; i 22 =  i  -  i =20.6  m. Regarding the applied torque, a nominal value M t =1543 Nm was assumed (the chosen value does not affect the generality of the results). The values used in the simulation, again equidistant from the average value and each other distant 2  , were M t1 =1651 Nm and M t2 =1442 Nm , with corresponding tractions on the external hub surface (Fig. 2) respectively equal to t 1 =4.28 N/mm 2 and t 2 =3.74 N/mm 2 . For the static friction coefficient that, as a control factor, was tested on two nominal levels f 1 =0.2 and f 2 =0.1 , the corresponding levels of the noise factors were obtained with a variation of +/- 7% from such nominal values: f 11 =0.214 and f 12 =0.187 , f 21 =0.107 and f 22 =0.0934 , respectively. Together with the static friction coefficients, also the dynamic friction coefficients were provided as input to the analysis: the latter were assumed 20% lower than the static ones. With reference to the geometry of the coupling, two different polygonal shaft-hub joints with three lobes were analysed: the first with eccentricity e=2.05 mm and the second with e=3 mm . The trochoidal profile of the shaft was realised using the system Pro/ENGINEER (P.T.C.) [5] and imported into the calculation program through the IGES exchange format. The BE analysis was initially carried out both with reference to the 3D (Fig. 2) and 2D models (Fig. 3), but for the sake of simplicity, the numerical experiments were carried out with reference to the 2D model. Under the action of a static torque, applied to the outer surface of the hub, the coupling exhibits a 120° cyclic symmetry; consequently, in order to reduce the computational effort, the analysis was carried out on just 1/3 of the entire model, imposing the boundary conditions of cyclic symmetry. One end of the shaft was assumed to be clamped whereas the torque M t was introduced on the hub by means of tangential forces. Figure 2 : 3D polygonal coupling with highlight of boundary conditions. The two models considered (A and B) had the following common dimensions (Figs. 1, 4): hub external diameter D h =87 mm , diameter of the circle inscribed to the profile D i =60 mm , hub length L 2 =32.5 mm . The differences between the two models were related to: