Identification of dynamic coefficients in circular journal bearings from unbalance response and complementary equations

Abstract

Experimentation is an effective approach to study the dynamic coefficients of journal bearings because experimental results are more reliable than theoretical calculations. Dynamic coefficients identification based on the unbalance response is more easily implemented than other experimental methods because of its independence from external exciting devices. However, this method may involve an ill-conditioned matrix problem, which increases algorithm complexity and decreases the precision of identification results. In this paper, a novel method is proposed to avoid ill-posed problems in the coefficient identification of circular journal bearings based on the unbalance response. The main approach used to overcome the ill-conditioned matrix problem is the introduction of four complementary equations that are uncorrelated with the dynamic equations derived from the unbalance response. Two relational expressions between damping are deduced from the Reynolds equation, and the other two relations between stiffness are obtained from the Taylor expansion of static forces acting on journal bearings. With the use of the four complementary relations, the identification matrix has a low condition number, and the identification of circular journal bearing dynamic coefficients can be easily implemented. Numerical experiments on two-axial groove journal bearings are used to analyze the condition number and identification error as well as verify the efficacy and accuracy of this method. The results show that the proposed method has a good identification capability with high precision and low condition number in solving the identification problems of journal bearings.

Keywords

Reynolds equation journal bearing dynamic characteristics condition number complementary equations hydrodynamic lubrication

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