Epicyclic System Research Articles

LOAD SHARING ANALYSIS OF PLANETARY GEAR BOX

One of the advantages of epicyclic transmissions is that the input torque is divided in a number of parallel paths. For n planet epicyclic system, each sun–planet–ring path is to transmit 1/n of the input torque. However, this is only true in the ideal case when there is equal load sharing between all the planets in the epicyclic system. Because of manufacturing errors, equal load sharing is not possible and the degree of inequality in load sharing has major role for gear system sizing, tolerancing schemes, and torque ratings. Therefore it is important to understand the fundamental cause of the unequal load sharing behavior in epicyclic gear sets. Load sharing behavior is associated with positional errors causing one or more planets to lead or lag the other planets. When the error is positive the planet with error lead the other planet while when the error is negative planet with error lags the other planet. Several manufacturing errors can introduce positional errors. Some of the common contributors are carrier pinhole position error, planet size variation, and run out of the gears. A set of precision planetary gear set is selected with the objectives of experimental and theoretical investigation of the load sharing behavior by introducing the position errors for the planets, the load shared by each planet is estimated by maximum stresses induced in each pin. The results of the experimentation are then validated with the FEM (Finite Element method) results.

Power Analysis of Epicyclic Transmissions Based on Constraints

Epicyclic gear transmissions have many applications. The internal power flow of epicyclic systems is highly related to the power loss of the system. A systematic method and generic formulas based on kinematic constraints are derived to conduct the power flow analysis, by means of Lagrange multipliers and newly introduced selection matrices. The method and formulas can be readily applied to complicated epicyclic systems. The graphic representation of the power flow of two examples verifies the balance of the power flow and virtual power flow. In the example of the Dual-E powertrain for hybrid electrical vehicles, an estimation of the total efficiency is derived. The pattern of contour maps of the total efficiency indicates the operational ranges of the powertrain with relatively low power losses.

Epicyclic Load Sharing Map — Development and validation

Under ideal conditions, every sun–planet–ring path in an epicyclic gear set transmits the same amount of torque. But, in the presence of certain manufacturing variations, equal load sharing is not achieved. In a companion paper, a physical explanation has been provided for the load sharing behavior observed in epicyclic gears. The explanation of the root cause led to the development of a load sharing formulation for 3, 4, 5, and 6 planet epicyclic systems. In this paper the same approach will be taken to develop the formulation for a seven planet epicyclic gear set. The developed expressions will then be used to develop the concept of an Epicyclic Load Sharing Map. This map describes the load sharing characteristics of every epicyclic gear set at any positional error and torque level. The developed expressions are then expanded to describe the general case when there are arbitrary errors on the position of every planet in the epicyclic gear set. Finally, the developed expressions will be validated by comparing the predicted load sharing behavior with the results from a validated system level computational model.

Load sharing behavior in epicyclic gears: Physical explanation and generalized formulation

Abstract In an n planet epicyclic gear set, under ideal conditions, each path will carry an equal amount of torque and therefore can be designed to transmit only 1/ n of the input torque. However, earlier works have shown that such equal sharing of the input torque between the parallel paths is not realized in practical applications, due to the presence of manufacturing errors. While various aspects of the load sharing behaviors have been shown both through computational models and experiments, a physical understanding of the true nature of the load sharing behavior is still lacking. In this paper, a physical explanation will be provided for the basic mechanism causing the unequal load sharing phenomenon. Both floating (system with clearances) and non-floating systems will be treated. On the basis of the physical explanation, closed form non-dimensional equations that predict the planet to planet load sharing behavior in the presence of positional errors will be derived. Epicyclic systems having 3–6 planets will be specifically treated and generalized equations for systems having an arbitrary number of planets will be presented. The developed expressions will be validated by comparing their predictions with previously published predictions from a computational model and experimental data.

Virtual-Power Flow and Mechanical Gear-Mesh Power Losses of Epicyclic Gear Trains

The concept of virtual power is first defined as the power measured, in a noninertial frame, in an epicyclic gear train. We then introduce the concept of virtual-power ratio, an invariant related to the power loss in an epicyclic system. It is shown that virtual-power flow and balance exist in an epicyclic gear train, based on which a novel algorithm to compute the gear-mesh powerloss and the train efficiency is formulated. This algorithm is general enough to be applied to any given epicyclic gear train. Our results are compared with previous work on the subject.

Triple Epicyclic Four-Clutch Six-Ratio Change-Speed Systems

Orthodox epicyclic change-speed gearboxes are not optimized to produce the maximum number of ratios from a given number of clutches and gear-sets. A class of triple epicyclic mechanism has been derived which meets this goal, and 2692 structural variants have been elucidated, grouped in 28 families. The topology of epicyclic systems has been studied to ensure that these variants may be constructed, and a systematic procedure has been set out to determine which of them will suit any particular purpose. Two examples are given.