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138 Ion Bostan et al 3. Calculation by CAE Simulation of Kinetostatics Parameters of Processional Transmission 3.1. 3D Model elaboration of Planetary Processional Transmission Calculation of planetary processional transmission by a simulation is carried out using the simplified 3D model created in program Motion Inventor 2004+ but (4) from which it is possible to determine and check up dynamic loadings in bearings which have been designed earlier. Dynamic processes in planetary processional transmission derive, to a great extent, from the interaction of conical rollers of the satellite crowns with generating surfaces of central wheel teeth. The bearing capacity defined by gear forces (static and dynamic), the noise emission and the transmission vibroactivity, depend on the gear dynamic processes on the whole. With account of these important factors in the elaboration of 3D model of the initial processional gearing, the linear contour of central wheel teeth profile (fig. 3, a) were designed applying parametric equations: (2) Where: X = k Z + d ; Y k Z d ; (k d = k d ) − m m m m 1E 2 1E 2 m 1E = m 1 m 1E − m 1 m Z1E m m m m 1 1 − 2 2 m2 m2 k1 + k2 + 1 (k d − k d ) + (k + k + 1) ⋅(R −d−d ) Z , m m m m 2 m2 m2 2 m2 m2 m 1E = 1 1 2 2 1 2 m2 m2 k1 + k2 + 1 D 1 2 ⎛ ⎞ • • • m m m m m m 2 m X1D⎜X1D X1D+ Y1DY1D⎟ + Z1D X1D + m m 1 = ⎝ ⎠ 2 = − • • m m⎛ m m m m ⎞ X1D Z1DX1DY1D−Y1D X1D k ; k ⎜ ⎟ ⎝ ⎠ 2 m m ( Rcos D β + dY 1 1D) • 2 m m Rcos D β X1D 1 = • • ⎛ m m m m⎞ X1DY1D− X1DY1D m 2 = m X1D d ; d . ⎜ ⎟ ⎝ ⎠ m m m ( kY 1 1D Z1D) The 3D model of the central wheel (fig. 3, b) was designed by using CAD Autodesk Inventor (5) (B o s t a n et al, 2007). ;
Bul. Inst. Polit. Iaşi, t. LVI (LX), f. 2, 2010 139 a. b. Fig. 3 – 3D linear contour of the central wheel teeth (a), and the model 3D of the central wheel (b). The 3D model for calculation is shown on fig. 4, it includes a crankshaft 1, a fixed wheel gear 2, the block satellite 3, a mobile wheel gear 4 rigidly connected with output shaft 5. Fig. 4 – 3D Model of planetary processional transmission. The dynamic model has been created on the basis of rigid model. As the initial data has been specified speed on input shaft [deg/sec] and the moment of torsion on the output shaft [Nm]. Kinematic joints fig. 5, have been enclosed according to movements in gearing. The crankshaft and the case of a reducer by means of cylindrical roller bearings are connected by a cylindrical joint to an opportunity of a selfcentering. A crankshaft and the block satellite by means of two tapered bearings with pair rotation in points of the appendix of loading on bearings (point-line), pair rotation (revolution) rollers on an axis of the block satellite and 3D contact of rollers to a mobile and fixed wheel gear.
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BULETINUL INSTITUTULUI POLITEHNIC D
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Papers presented at THE INTERNATION
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