Efficiency of gear trains determined using graph and screw theories

A new method to determine the efficiency of complex gear trains based on graph and screw theories is presented. This method can be applied to any gear train where the gear axes are parallel (cylindrical gears) or intersecting (bevel gears). The Daviesʹ equations are modified to include mechanical analogues of the electrical resistance and dependent source aiming at the modelling of friction. Loss sources like gear meshing friction, bearing friction and seal friction can be taken into account. Friction models can include load and speed-dependent effects. The relationship between friction model and ordinary efficiency is, possibly for the first time, elucidated. It is also proved that the action responsible for power losses in gearing is a pure torque under certain commonly encountered conditions. Three examples are presented and the results are compared with those of previous studies. Application of the method in other areas of mechanical engineering is straightforward.