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140 Ion Bostan et al Fig. 5 – Kinematics joints in the planetary precessional transmission. 3.2. Precessional Transmission Kinetostatic Simulation The simulation of model processional gearings has been created in some stage. At the first stage has been executed the kinematic analysis, from definition of the following parameters: transfer ratio, absolute angular speed of the block satellite, relative angular speed of the block satellite, angular speed on the output shaft. The received results are shown on Fig. 6. Fig. 6 – Kinematic calculation of planetary processional transmission. At the following stage has been executed the kinetostatics analysis with calculation and simulation of total loadings in gearings.
Bul. Inst. Polit. Iaşi, t. LVI (LX), f. 2, 2010 141 An important advantage of the processional planetary transmission consists in the insurance of absolute multiplicity (ε=100%) of the central wheel teeth and pinion simultaneous gearing. This advantage provides small dimensions and mass (reduced material consumption) and small cost of the final product. a. b. Fig. 7 – Normal forces among the teeth and their distribution among simultaneously geared teeth. The vertical line on the diagram (Fig. 7) shows the precession phase reported symbolically to the gearing time of the pinion tooth with the central wheel tooth (as reference the time was taken, because as CAE input parameters the angular ω velocity was introduced). On the diagrams one can see the distribution of load among the teeth which corresponds to the respective precession phase (blue colour – distribution of load on the active profile of central wheel tooth, red colour – per one precession cycle). It is possible to state from the diagrams that despite the precession phase, the load among teeth is uniform. Due to load transmission from the input shaft to the output shaft by a big number of teeth couples geared simultaneously ⎛ (Z − ⎜ = 4 1) ε ⎞ ⎝ 2 ⎟ the normal ⎠ forces at teeth contact are much smaller as in the classical transmissions with in volute transmission. 4. Conclusions 1. Taking into account the fact that in processional planetary gearings the (Z4 − 1) teeth couples transmit the load simultaneously we can conclude that 2 the bearing capacity of the processional gear is much bigger than that of the classical in volute gear (in which only 5...7 % of wheel teeth gear simultaneously).
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BULETINUL INSTITUTULUI POLITEHNIC D
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CONSTANTIN CHIRIȚĂ, ADRIAN HANGAN
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