Baldor 23H Series Installation & Operating Manual page 142

Consider matching load and motor inertia. The following
presents some points to consider.
System performance depends upon the load and motor coupling, and the ratio selected. These
determine response, mechanical resonance, and power dissipated.
Response
Typical system response with "relatively good inertial matching" is shown in Figure 1. As the load
to motor mismatch is increased, oscillations occur, and it takes longer to settle in position
(Figure 1b).
The fix, to prevent oscillation and overshooting, is to lower the gain and extend the settling time
(Figure 1c). This leads to lower accelerations and slower positioning. This approach may not be
acceptable for some applications.
Special loop compensation, of course, can be designed. This would allow handling of higher
inertial mis-matches. However, this leads to highly custom designs and now standard off the shelf
controls cannot be used.
Mechanical Resonance
Analyzing the transfer function of the load, motor shaft, and feedback device, the resultant
equation is:
f = 1 (J + J ) K
L M
2π J J
L M
Where J is the load inertia, J
L
This equation provides the frequency of the mechanical resonance. It points out that the torsional
resonance 1) depends upon the load and motor coupling, i.e. the transmission stiffness and 2) the
frequency point is lower for high inertia loads.
For the best response, this resonant point should be outside the system bandwidth. It is typical to
have the resonant frequency 5-10 times the servo loop bandwidth due to rise time requirements.
The easiest, quickest, and least expensive method is to use gearing, or a larger motor (with more
inertia) to improve the inertia ratio.
Power Dissipation
Analyzing the equation for energy dissipation for optimum versus non-optimum ratios, the resul-
tant analysis is plotted in Figure 2. This show the amount of additional system energy dissipated as
mis-match increases. It indirectly also reveals the additional current required (by the square root).
The plot reveals that a small deviation from optimum is not critical, however, as the deviation
increases, the penalty becomes increasingly severe. As can be seen, the ratio of 1:1 provides for
Application Notes
Inertia Matching
is the motor inertia, and K is the transmission stiffness.
M
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