Conceptual Design Of Compound Gear Trains Using Energy Characteristic State Method

A new methodology for modeling of compound gear trains using energy equations is established, by which the method of modeling of gear trains, power flow analysis and conceptual design is proposed, based on Characteristic State Space Theory.Energy vectors of which there are two items referring to kinematics and kinetics respectively are established for modeling of rotatory links of gear trains. Kinematics equations and kinetics equations of gear trains are developed based on the energy vectors. Using energy equations the characteristic equations are established, which are the energy characteristic model of gear trains.Basic units of gear trains are defined, modeled using characteristic equations and stocked in the basic unit database. Based on the research of unit connecting the different patterns of links in units and the variation of degree of freedom in the combination of units are compiled. Energy transfer equations are established for energetically modeling the combination of units. From the energy transfer equations of the combination of two units the general Energy transfer equations are derived.Basic combination patterns such as combining in serial and in parallel are studied of which the energy models are the coalescence of characteristic equations and energy transfer equations. Then compound combination patterns are studied of which the energy models are the energy equations and additional equations. With the equations the modeling of the serial, parallel and hybrid combination of units is complemented, and the energy analysis method of gear train is developed.Conceptual design method of gear trains basted on unit groups is presented. With the definition of unit group, gear trains are classified into two distinct types: ordinary gear trains and complex gear trains, according to the different forming types. Structure vectors are defined and the mathematic model of the synthesis of gear trains is presented basted on gear structure vectors. Using the structure vector system connection matrix is mapped and unit characteristic matrix is mapped into system characteristic matrix. The equations to solve based on the matrices is achieved.