Theory for Backlash
The Backlash node can optionally be added on gear pairs. The transmission error due to backlash is added in the rotation constraint of the gear pair. By default, there is no backlash on a gear pair.
The backlash on a gear pair plays an important role for unloaded gears. For loaded gears, it does not affect the dynamics of gears to a large extent.
The backlash is taken into account only in the case of a time-dependent analysis.
Figure 3-24: Sketch of a pair of teeth, showing the point of contact and the direction in which backlash is interpreted.
The transmission error (backlash), θbl, is degree of freedom in this node. The backlash moment about the first axis of the tooth coordinate system and its virtual work contribution are defined as:
where bl and pbm are the backlash and modified penalty factor, respectively.
To prevent the solver from taking larger time steps, the penalty factor is modified in the following manner:
The penalty factor is not modified for quasistatic analysis or when the manual control on time stepping is deselected.