Inertia mismatch: fact or fiction? Is this often-quoted concept an excuse for inadequate system modeling?

摘要

Servo systems may be direct drive or geared. For geared systems, the motor selection also involves a choice of gear ratio. Figure 1 shows a motor connected to a load through an ideal (that is, no friction, no backlash, and no compliance) gear train with gear ratio N. The equation of motion for this one-degree-of-freedom system is shown in terms of the load angular velocity, ω_L. The inertia ratio is the ratio of the load inertia to the motor inertia, J_L/J_M. What is the optimum value of this ratio for a particular value of N? If you ignore' the motor and load damping, B_M and B_L, respectively, and the load torque, T_L, the inertia ratio that maximizes the power transferred from motor to load is N~2 - that is, the reflected motor inertia equals the load inertia. When friction and load torques and system compliance (for example, coupling or timing-belt compliance) are significant, the selection of an optimum inertia ratio is less straightforward. Figure 2 shows this more general case.