Invariant points of semi-active suspensions

The invariant points of the quarter vehicle model shape many properties concerned in vehicle suspension design. Although they have been studied for years, the invariant points are still confusing for their different traits. Hence, the existing invariant points are sorted and analysed. Meanwhile, the invariant points of the semi-active suspension were introduced. In this article, a further study on the invariant points of the semi-active suspension is conducted, which provides insight for suspension optimization. In detail, an equivalent linear approximation model, derived from the transformation of the semi-active suspension model, is utilized to analyse the invariant points of the semi-active suspension. With the equivalent linear approximation model, the invariant points of the sky-hook semi-active suspension are proved to be highly dependent on the adjustable damping range. In fact, the frequencies and magnitudes of the invariant points, as the limit of the semi-active suspension, are determined by the adjustable damping range. Consequently, the influence rule of the adjustable damping range on semi-active suspension performance is revealed, which provides insight for the optimization of the damping for different demands. Experimental study shows that the invariant points are real, not just exist in the theoretical analysis.