CSV-Based Evaluation of Dynamic Stiffness


The application area of the collinear stiffness value (CSV) developed for the static case [1, 2] can be extended to dynamic characteristics of the mechanical system modeled as a massive rigid body (platform) on elastic supports in a current configuration [3]. Here, this approach is applied to evaluation and optimization of the dynamic stiffness of undamped systems using a modified CSV index named the dynamic collinear stiffness value (DynCSV). The minimal value of the DynCSV is used for limitation of the machine and robot workspace and frequency bandwidth. The most important aspect of the proposed approach is that it allows construction of a virtual protective barrier preventing, if necessary, approaching the resonance zone. In the dynamic case, the CSV-based index can be applied taking into account that:

  • The dynamic-related characteristics become both configuration- and frequency-dependent;

  • The zero values of the DynCSV can take place not only in singular configurations as in the static case, but also when a statically regular configuration (with w = 0) falls within one of the natural frequencies;

  • The derived method allows a natural evaluation of the dynamic stiffness for the general case of loading, i.e., for any combination of decoupled translational and angular vibrations. Hence, the allowable workspace of the robot can be limited using the stiffness values instead of traditional methodology when approaching the vicinity of the resonance zone is limited based only on a distance (expressed in w-terms) from the natural frequencies;

  • The DynCSV presents a convenient optimization tool using stiffness-related properties under the general case of the loading, since it estimates the dynamic properties over the entire bandwidth forced frequencies including the natural frequencies, while application of the natural frequencies is an excellent tool for establishing conditions resulting in zero stiffness values, but unsuitable for stiffness evaluation in other conditions.

5.2Dynamic collinear stiffness value
5.4Brief discussion
Topics: Stiffness

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