You have the data flow backward. Ansys Mechanical doesn't estimate damping ratios. Physical testing measures damping ratios and those measured values are used as inputs to the Ansys model that estimates the system response to vibration loads.
Once you measure a damping ratio, there are equations to calculate the Rayleigh Damping coefficients, but if you use Modal Superpostion methods, you can use the damping ratio directly and use a different value for each mode.
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