Methods to determine composite vibration indices of a drilling assembly

1. A computer implemented method to drill a borehole within a subterranean formation with a drilling assembly, the method comprising the following steps:

selecting a lateral, torsional, or axial mode frequency-domain dynamic model of the drilling assembly, wherein the dynamic model describes a dynamic response of the drilling assembly to excitation at an excitation frequency for operating at a set of selected drilling parameters that include at least a rotary speed and a weight on bit;

providing a non-transitory machine-readable storage medium having stored thereon a routine of set instructions for using the selected frequency-domain model and for causing the machine to perform one or more of the steps of;

calculating the dynamic response of the dynamic model for an excitation of the drilling assembly for at least two excitation frequencies for each of at least two sets of selected drilling parameters;

calculating vibration indices from the calculated dynamic model response to represent the system output for each of the at least two excitation frequencies for each set of drilling parameters;

receiving data measurements from at least one drilling operation that includes measurements pertaining to the excitation of the selected dynamic model;

identifying drilling parameters in the measured dataset that correspond to the selected model drilling parameters;

determining drilling parameter partitions of the data measurements for the selected drilling parameters;

calculating at least one frequency domain spectrum of the data measurements for each of the partitions;

determining for each of the partitions, from the at least one calculated frequency domain spectrum, spectral weighting factors based at least on the spectral amplitude at each of the two or more excitation frequencies in the at least one spectrum;

calculating a composite vibration index by combining the calculated vibration indices for each excitation frequency with the spectral weighting factors for each of the drilling parameter partitions;

displaying said composite vibration index for each of the drilling parameter partitions;

selecting preferred drilling parameters based on the displayed results;

and

using the preferred drilling parameters to drill a borehole with the modeled drilling assembly.

2. The method of claim 1 wherein spectral weights are determined for at least two partitions of drilling operating parameters.

3. The method of claim 1 wherein the drilling operating parameters include at least rotary speed and drilling rate of penetration.

4. The method of claim 1 wherein the drilling operating parameters include at least rotary speed and surface drilling torque.

5. The method of claim 1 wherein the spectral weights are constant values determined for a plurality of combinations of rotary speeds and bit weights for which the cutting fact of the drill bit is in contact with the formation and making new hole.

6. The method of claim 1 wherein the spectral weights are determined for the condition when a cutting face of the drill bit is rotating off bottom.

7. The method of claim 1 wherein the excitation frequencies comprise a fundamental harmonic frequency that is synchronous with the rotary speed of the drilling assembly and at least one harmonic multiple thereof.

8. The method of claim 1 wherein at least two drillstring assemblies are modeled and the results are displayed for each modeled drillstring assembly, wherein one drilling assembly is selected based on the model results, and further wherein the selected drilling assembly is used to drill a borehole.

9. The method of claim 8 wherein the same spectral weighting factors are used for each model of the at least two drilling assemblies.

10. The method of claim 8 wherein at least two different spectral weighting factors are used for each of the models of the at least two drilling assemblies.