Dynamics of a Mechanical Drive

The equations derived in Chap. 1 (2.1)$$J\frac{{d\omega }}{{dt}} = {{m}_{M}}\left( {\omega ,{\mkern 1mu} {\mkern 1mu} \varepsilon ,{\mkern 1mu} {\mkern 1mu} {{y}_{M}},{\mkern 1mu} {\mkern 1mu} t} \right) - {{m}_{L}}\left( {\omega ,{\mkern 1mu} {\mkern 1mu} \varepsilon ,{\mkern 1mu} {\mkern 1mu} {{y}_{L}},{\mkern 1mu} {\mkern 1mu} t} \right)$$, (2.2)$$\frac{{d\varepsilon }}{{dt}} = \omega$$, describe the dynamic behaviour of a mechanical drive with constant inertia in steady state condition and during transients. Stiff coupling between the different parts of the drive is assumed so that all partial masses may be lumped into one common inertia. The equations are written as state equations for the continuous state variables ω, ε involving energy storage; only mechanical transients are considered. A more detailed description would have to take into account the electrical transients defined by additional state variables and differential equations. The same is true for the load torque m _L which depends on dynamic effects in the load, such as a machine tool or an elevator.