ESSAM LAUIBI ESMAIL
College of Engineering/University of Qadisyah
Planetary gear trains (PGTs) are introduced to undergraduate mechanical engineering students in the course of Theory of Machines. The complexity of the traditional methods for analyzing PGTs has kept many from becoming familiar with the capability of PGTs in mechanisms and machine design. In this paper a unified general formulation for simultaneously visualizing velocities, torques and power flow through a train is presented on a single nomograph. Therefore, the increasing complex mechanical systems, such as automotive transmissions, are much easier to understand.
Nomographs of Fundemental Gear Entities (FGEs) are constructed based on the nomographs of their fundamental circuits, without specifying the exact gear dimensions. They are then unified in one system nomograph. Nomographs are promising to provide designers an efficient tool for the design of geared mechanisms.
KEYWORDS: Fundamental Circuit, Fundamental Geared Entity, Graph Theory, Mechanisms, Nomograph, Power Flow, Planetary Gear trains, One-Degree of Freedom. NOMENCLATURE
Distance from origin to the point of intersection of the horizontal axis connecting the zeros of the three axes of a nomograph with the straight line passing through operating velocities of a fundamental circuit EGM
Epicyclic gear mechanism
Epicyclic gear train
k th Fundamental circuit
Fundamental gear entity
Geared kinematic chain
Gear ratio defined by a planet gear p with respect to a sun or ring gear x. N p,x
N p , x = ± Z p / Z x , where Z p and Z x denote the numbers of teeth on
the planet and the sun or ring gear, respectively, and the positive or negative signs depend on whether x is a ring or sun gear.
One way clutch
Planetary gear train
Velocity ratio between links x and y with reference to link z Horizontal distance from origin to any point on the straight line passing through the operating velocities of a fundamental circuit
T ga , k , T gb , k
and T c , k
External torques exerted on links ga, gb and c of the k th Fundamental circuit or exerted on link i
Two-degree of freedom
Number of teeth on gear i
Angular velocity of link i
INTRODUCTION AND LITERATURE REVIEW
Epicyclic gear trains (EGTs) are commonly used in automatic transmission mechanisms to achieve a set of desired velocity ratios (Tsai, 2001). Figure 1 shows an epicyclic gear mechanism employing the Ravigneaux gear set as the ratio change gear train where the rotating and band clutches are designed as C and B, respectively. The velocity ratios selected for a transmission are tailored for vehicle performance. Typically, they include a first gear for starting, a second or third gear for passing, an overdrive for fuel economy at road speeds and a reverse (Hsieh and Tsai, 1996). Table one shows the clutching sequence for the transmission shown in Fig. 1.
Figure 1 A typical automatic transmission mechanism.
Table 1 Clutching sequence for the transmission shown in Fig. 1.
For downhill braking only.
For the kinematic analysis of EGMs, various approaches such as the relative velocity method [13, 19, 20], energy method (Wilkinson, 1960), bond graph method (Allen, 1979), vector-loop method [14, 29] and the nomograph method [4, 26, 9] have been proposed. (Freudenstein and Yang, 1972) introduced the concept of fundamental circuit to analyze EGTs. The concept was further extended by other researchers [22, 16]. The concept of fundamental circuit is a powerful tool for automated analysis of EGTs. In addition, some other studies have concentrated on structural and dimensional syntheses [2, 5, 6, 17,...