Dynamic Behavior of Planetary Gears

Besides power density, reliability and efficiency, noise is always an important criterion for a successful gear design. In many theoretical and experimental investigations and papers, the influences and potential remedies were discussed. For example, in (Ref.6) the importance of a large overlap ratio, achieved by a large helix angle is described as the most important factor for reducing gear noise. In planetary gear systems of high power density and high gear ratio, helical gears create undesirable tilting moments on the planet gears; therefore, spur gears are still preferred for planetary gears—a special challenge with respect to noise. Specifically, the different behavior of planetary gears with sequential and symmetric gear mesh is explained in this paper. As described (Ref.10), the variable mesh stiffness along the path of contact in the tooth contact leads to oscillating forces on the shafts and bearings, which are transmitted to the casing. The casing vibrations radiate airborne noise (Fig.1). The influence of tooth geometry on the excitation behavior is determined by the geometry parameters, such as profile and overlap ratios, flank modifications and manufacturing deviations. For design to low noise emission, the knowledge of the elastic and dynamic behavior of the transmission system and the excitation mechanisms of the gear mesh is required. Parameters which are useful to evaluate the dynamic behavior of a gear mesh are described in this paper. The findings of (Ref.10) are summarized in this paper, further developed and, for sequential gear mesh, applied to a practical example with test stand measurements. Hereby, the theory is further sustained on how several variables impact gear noise in parallel shaft and planetary gear trains.

Gear Mesh Excitation

For a cylindrical, involute gear mesh, the main parameters of excitation are: ? Time-varying tooth stiffness ? Deflection of the teeth ? Deviations in tooth geometry ? Deflection of shafts, bearings and casing ? Premature tooth contact under load Tooth deflection and mesh stiffness. Single tooth mesh stiffness consists of three components as depicted in Figure 2: ? Tooth deflection due to bending under load ? Bending deflection of the gear blank or gear rim ? Contact deflection of surfaces under Hertzian stress Even with close to perfectly manufactured gear geometry, due to this elastic deformation under load, the flank position will shift relative to the theoretical unloaded position (Ref.5). There will be interference between the gear teeth with the subsequent, not-yetloaded gear teeth, which are about to enter the mesh (Fig.3), causing periodic noise excitation. This interference can be compensated for by appropriate profile modification, which only can be optimized for one load level. If not addressed appropriately, the subsequent teeth will come into contact prematurely outside the path of contact (“premature gear mesh”) and may cause stretch marks (Fig.3). Dynamic excitation. Even with perfect profile modification preventing an interference between the mating gear teeth entering the gear mesh, the total mesh stiffness varies considerably along the path of contact. This is caused by the influences as described in Figure 2 and, moreover, in the change between single and double tooth contact along the path of contact. Especially for spur gears, two indicators for excitation can be derived from this change of stiffness (Fig.4): ? Transmission error, which is the static deflection between pinion and wheel under load, ignoring mass acceleration forces, and describes the oscillation of output speed at constant input speed. ? Force excitation, which is the maximum dynamic force created by the transmission error without compensating movement of masses (i.e., rigid masses). It may be used as the force parameter to evaluate the level of excitation, but does not, however, consider the real dynamic system.