No abstract

The features of the support structures of the sun gear, carrier and ring gear that are the components of a planetary gear set result in large alignment error in the form of eccentricity or inclination. Such error causes the relative tooth flank error to vary periodically at each pinion position. The side band phenomenon modulated by the rotation of the rotating elements appears around the mesh order components of transmission error. With the conventional method of calculating transmission error, it is not possible to evaluate the side band phenomenon because of the inability to treat the periodical variation in the relative tooth flank error. Therefore, we have developed a new method of simulating the transmission error of planetary gear sets taking into account such periodical variation of the eccentricity and inclination direction of each element. The predicted values are then input into the calculation, making it possible to evaluate the side band phenomenon as well. Periodical variation in the relative tooth flank error due to alignment error returns to the original state when the relative rotation between the rotating elements has completed one revolution. Accordingly, by repeating the calculation until the relative rotation between the sun gear and the carrier or between the carrier and the ring gear has completed one revolution, the new method makes it possible to analyze transmission error taking into account the periodical characteristic of the shape of the tooth flank error due to alignment error. This new calculation method was applied to analyze the transmission error of an actual transmission, and the results showed that the side band phenomenon was also evaluated with relatively good accuracy.

The conical involute gears have been applied to automotive parts such as 4WD transfer. The conical gear pair has characteristic large ease-off and this is equivalent to meshing of cylindrical gears which has large crowning for lead direction. Consequently, the trochoidal interference is thought to be caused because of tooth stiffness reduction. In this study, to clarify the influence of the tooth flank modification on the tooth surface damage, tooth surface endurance test with several tooth flank modification forms is experimented. As a result, the gear pair with crowning for tooth profile direction and reverse crowning for lead direction can extend the pitting fatigue life because of the edge load reduction of tip or root.

In this paper, the characteristics of traction grease are evaluated. The difference in film formation ability between traction oil and traction grease is focused on, and the state of film formation and the traction coefficient of traction oil and two types of traction grease with different consistencies are measured simultaneously while varying temperature, Hertzian pressure and rolling speed. The traction coefficient of traction grease at a low temperature, a low pressure and a high peripheral speed shows a value larger than that of traction oil. The film thickness of traction grease is measured by the contact ratio method and decreases markedly at a low temperature and a high peripheral speed compared with that of traction oil. An estimation formula for traction grease considering film thickness is developed. These results lead to the conclusion that the property change between traction oil and traction grease is caused by the change of the film formation state.

The mechanism of the sideband phenomenon of planetary gear vibration that often occurs in a planetary gear set was clarified in connection with mesh phase differences. This sideband phenomenon is one in which the (Z-1) or (Z+1) order component level is higher than the mesh order (Z) component level. The notation (Z-1) or (Z+1) means the mesh order (Z) minus or plus one carrier revolution. An in-phase (IP) planetary gear set has no such sideband phenomenon. In a sequentially phased (SP) planetary gear set, this phenomenon occurs in transverse and tilting vibration of sun gear, carrier and ring gear. Which sideband, either (Z-1) or (Z+1), occurs depends on the relationship between the mesh phasing direction and carrier rotation direction. To verify this sideband phenomenon, we derived the formulae to calculate the translational forces in x, y and z directions and the rotational moments about these translation axes which act to sun gear, carrier and ring gear due to mesh forces at each mesh point.