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This paper is focused on the optimal selection of the parameters of a passive dynamic vibration absorber (DVA) attached to a boring bar. The boring bar was modeled as an Euler-Bernoulli cantilever beam and the stability of the system was analyzed in terms of the bar and the absorber characteristics. To obtain the optimum parameters of the absorber, a classical method for unconstrained optimization problems has been used. The selection criterion consisted of the maximization of the minimum values of the stability lobe diagram. Empirically fitted expressions for the frequency and damping ratio of the DVA (which permit to obtain its stiffness and damping) are proposed. These expressions are fully applicable when the damping ratio of the boring bar is non-null as it is in practical operations. The computed results show a clear improvement in the stability performance regarding other methodologies previously used.