Issue 30

G. Belingardi et alii, Frattura ed Integrità Strutturale, 30 (2014) 469-477; DOI: 10.3221/IGF-ESIS.30.57 472 The internal dynamic factor makes allowance for the effects of gear tooth accuracy grade as related to speed and load. High accuracy gearing requires less derating than low accuracy gearing.It is generally accepted that the internal dynamic load on the gear teeth is influenced by both design and manufacturing. “Perfect” gears are defined as having zero quasi-static transmission error at the nominal transmitted (design)mesh torque. They can only exist for a single load and, with proper modifications, have zero dynamic effectszero transmission error (perfect conjugate action), zero excitation, no fluctuation at tooth mesh frequencyand no fluctuation at rotational frequencies. With zero excitation from the gears, there is zero response at any speed [7]. The Internal Dynamic Factor K v takes into account the effects due to the rotating masses; ISO 6336 part 1 [7] suggests three methods for calculating this factor. Method A (K v-A ) derives from the results of full scale load tests, precise measurements or comprehensive mathematical analysis of the transmission system and all gear and loading data shall be available, then this method, in this work, corresponds to the dynamic multibody analysis results. Method A generally results the most sophisticated. Method B (K v-B ) is suited for all types of transmission, spur and helical gearing with any basic rack profile and any gear accuracy grade and, in principle, for all operating conditions. Method C (K v-C ) supplies average values which can be used for industrial transmissions and gear systems with similar requirements, with restriction in the application field. In the present paper Methods B (K v-B ) and C (K v-C ) have been taken into account as the resolution of the corresponding equations described in detail in [7]. K v-B coefficient has been calculated on the basis of the different operating ranges (subcritical, main resonance, intermediate and supercritical ranges) related to the resonance ratio N of the mating gears [7]. Firstly, the resonance running speed of the gear pair n E1 has been determined as a function of the reduced gear pair mass per unit face width, of the mesh stiffness and of the pinion number of teeth, as indicated in detail in [7]. Then the resonance ratio N, where N=n 1 /n E1 , has been calculated, being n 1 is the rotational speed of the pinion in rpm. Once the resonance ratio N has been obtained, the operating range has been determined as a function of the specific load Ft· K A / b, according to [7],where Ft is the tangential load, K A the application factor, b the gear face width and Ns is the lower limit of the main resonance range. The dynamic factor K v-B has been computed for the different ranges, following the involved relationships indicated in [7]; non-dimensional parameters which take into account the effect of tooth deviations and profile modifications on the dynamic load are considered. In particular, it has been calculated for: subcritical range N ≤ N S (the majority of industrial gears operate in this range), main resonance range N S <N ≤ 1.15 (operation in this range should generally be avoided, especially for spur gears with unmodified tooth profile or helical gears of accuracy grade 6 or coarser, because the dynamic forces could be very high), supercritical range N ≥ 1.5 (most high precision gears used in turbine and other high speed transmissions operate in this range), intermediate range 1.15 <N< 1.5(the dynamic factor is calculated by linear interpolation between K v at N = 1.15 and K v at N = 1.5). According to method C [7], the dynamic factor K v-C has also been obtained as a function of the specific load (as K v-B ), of the accuracy grades for spur and helical gears and of the tangential speed, without any attention to the operating ranges. R ESULT AND DISCUSSION btained results are presented in this paper in terms of comparison between K V values related to the different calculation methods. For as concerns the Methods BISO 6336 [7], specific loads, resonance ratios, lower limits of main resonance range and corresponding K v-B values for each electric motor speed are reported in Tab. 2; in particular, in column one is indicated the motor speed in rpm, in the second column is reported the specific loading of the gears, in the third one the resonance ration, in the fourth one the resonance ratio in the main resonance range and in the last one the internal dynamic factor of gear 4. For as concerns Method C ISO 6336[8], since the specific load is always lower than 100 N/mm for each class, the dynamic factor is a function of the tangential speed only. So, for the maximum tangential speed v = 12.02 m/s, K v is equal to 1.21. Multibody Simulation allows to determine contact forces involved in the calculation of dynamic parameters. The contact force components versus time of Gear 4, obtained by the rigid simulation, are shown in Fig. 3; the forces directions are referred to the ground system of the model. O