| dc.description.abstract | Compared with the traditional parallel axis gear train, the planetary gear drives have the characteristics of coaxial input or output, compact design, high speed ratio, high power density, etc. Therefore the planetary gear drives are widely used in various types of transmission application, such as automotive gearboxes, wind turbines, increase and reduction gear drives, servo motor reduction gearboxes, etc. The multi-stage planetary gear drives have a wider range of speed ratios and power flow type due to the various connection relationship. However, some drives with special connection relationship will have characteristics that internal circulation power will be generated and as a result power loss will increase during power transmission. Such the characterics might cause the drives to self-locking.
The purpose of this paper is to investigate the transmission efficiency of four two-stage compound and coupled planetary gear drives under the influence of tooth surface friction. The study cases for compound planetary gear drives in this paper are so-called the 2K-H type and the 3K type paradox planetary gear drives. These two type paradox planetary gear drives having tooth number differences engage with the same planetary gear under the same center distance. If the thooth profile is designed using the traditional gear desigh method of standard datum rack and profile shifting, suitable tooth profile design parameters can not be obtained. Therefore, this paper adopts the direct tooth profile design method, where the addendum and tooth thickness on the working pitch circle are used as the design parameters, and the complementary tooth profile and pitch relation of the gear are also applied to obtain the essential relation of the geometrical parameters of the tooth pairs. The effective geometric parameter range can be thus constraint by the geometrical limits of tooth tipping and interference. The gearing parameters for the optimal load capacity of the gear drive can be further determined according to the root or surface strength of each gear pair. The coupled planetary gear drives include two cases: type Ⅰ where the first-stage carrier connects with the second-stage ring gear, and type Ⅱ where the ring gears of the two stages connect with each other.
In order to determine the efficiency, the relations for the speed and torque of the planetary gear drives at first established. The power flow direction of the drives can be thus deduced, so as to idebtify whether the drives generates internal circulation power. Because of the revolution motion in the planetary gear train, the meshing efficiency is introduced to obtain the average efficiency od the drives. In oder to further obtain the instantaneous efficiency of the planetary gear drives, the load analysis model of one-stage planetary gear set based on stiffness method is extened to analyze two-stage planetary gear trains with considering the influence of the friction on teeth. The meshing efficiency of each tooth pair ateach meshing step can be calculated, and the variation of the transmission efficiency of various planetary gear drives during meshing can be represented accordingly.
From the analysis results of the transmission efficiency of the planetary gear drives, it can be found that the amplitude of the instantaneous meshing efficiency will be reduced during the transmission, if the number of teeth of the planetary gear drives are configured as non-factorizing, namely the meshing is in non-equal phase angle. The compound planetary gear drives in the paper will produce internal circulation power flow. On the other hand, the coupled planetary gear will not generate such the phenomenon, but power splitting or summation in the differential stage. The internal circulation power flow of the 2K-H paradox planetary gear drive is about 19 times the external power. Therefore, the self-locking will occur, when the meshing efficiency is greater then 5% or more. However, the internal circulation power flow of 3K paradox planetary gear drive is about 7 times the external power. In the differential type of coupled planetary gear drives, the transmission efficiency of the type Ⅱ is about 94.1% under the friction coefficient of 0.15, which is higher than 85.7% of the type Ⅰ. The fluctuation amplitude of the instantaneous efficiency is also one-third of the type Ⅰ.
The analytical calculation model proposed by this paper can be used for various compound and coupled planetary gear drives to, analyze the variation of transmission efficiency under different friction coefficients. The results can be used to determine whether the planetary gear drives are self-locking during the meshing process. This apprach can provide an effective reference for basic design of such the types of planetary gear drives. | en_US |