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.
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