Power Flow in Coupled Three-Row Series-Parallel Planetary Gear System, Part I: Without Power Losses

Abstract

So far it is believed that, for every series-parallel planetary gear system (PGS), as a coupled gear, a very harmful phenomenon of power circulation must occur in at least one of its closed circuits. In this paper (Part I) and in the next two (Part II and Part III), it will be shown that it is possible to construct a three-row series-parallel PGS in which this phenomenon can be avoided. For this purpose, in Part I, a detailed analysis of the kinematics and statics of a planetary gear with power circulation inside a closed loop was carried out. The determination of the angular velocities of gears and carriers is carried out using Willis formulas and the graphical-analytical method (for verification), while the torques are determined using free body diagrams. The magnitudes of angular velocities and torques were used to determine the directions of power flows with improved energy balance equations in the reference frame related to the stationary gear body and, additionally, only to verify the energy balance equation in the mobile reference frame related to the carrier hi (i=2,5,8). The improvement of the methods was based on the use of the original concept of distinguishing active torque from reactive torque, as well as active power from reactive power, which made it very easy to determine the directions of the power flow. The determined paths of the power flow, including the power circulation in the analysed PGS, are presented graphically.

Power Flow in Pseudo-Coupled Three-Row Cylindrical Series-Parallel Planetary Gear Systems. Part II: Without Power Losses

“…It is not dynamically coupled due to the lack of power flow circulation. There is also no increase in the power ratio above 100%, which was a normal phenomenon in coupled PGS (Figure 9(b) [3]). It is proposed that PGS containing at least one closed circuit without visible dynamic coupling be called pseudo-coupled or semi-coupled.…”

“…The cylindrical PGS analysed in Part II (Figure 1(a)(b)) is very similar in structure to the PGS analysed in [3] (Figure 4(a)). It consists of two subsystems A and B in the form of solar-type units as elementary 2KH planetary gears and one star-type gear C -(Figure 2(a)(b)).…”

“…they contain 3 movable shafts and thus have two DoF each. Identification of the power flow paths in the pseudo-coupled PGS is carried out according to a similar algorithm used for the coupled PGS [3]. The values of the fixed carrier transmission ratios of subsystems A, B and C and pairs of sun and planet gears are listed in Table 3 based on calculations in Appendix A.…”

“…Due to their structure and parallel connection of subsystems, PGSs are characterised not only by multi-path power transmission but also by the phenomenon of power closure, commonly called power circulating inside, at least one parallel connected elementary subsystem in the form of a closed circuit. As demonstrated in papers [1][2][3], this phenomenon can be a source of even a large overload of gears, shafts and bearings of a closed subsystem. In the case of an unfavorable distribution of power on individual paths, an additional reduction in efficiency may be revealed.…”

“…< . Therefore, unlike the same subsystem B in coupled PGS [3], there is no phenomenon of circulation of the power stream. Table 13 shows that there is also no overloading of any of the elements of this and the next subsystem.…”