Development of linear and nonlinear hand-arm vibration models using optimization and linearization techniques.

Hand-arm vibration (HAV) models serve as an effective tool to assess the vibration characteristics of the hand-tool system and to evaluate the attenuation performance of vibration isolation mechanisms. This paper describes a methodology to identify the parameters of HAV models, whether linear or nonlinear, using mechanical impedance data and a nonlinear programming based optimization technique. Three- and four-degrees-of-freedom (DOF) linear, piecewise linear and nonlinear HAV models are formulated and analyzed to yield impedance characteristics in the 5-1000 Hz frequency range. A local equivalent linearization algorithm, based upon the principle of energy similarity, is implemented to simulate the nonlinear HAV models. Optimization methods are employed to identify the model parameters, such that the magnitude and phase errors between the computed and measured impedance characteristics are minimum in the entire frequency range. The effectiveness of the proposed method is demonstrated through derivations of models that correlate with the measured X-axis impedance characteristics of the hand-arm system, proposed by ISO. The results of the study show that a linear model cannot predict the impedance characteristics in the entire frequency range, while a piecewise linear model yields an accurate estimation.