Study of the external section shape of the static characteristic of the antivibration suspension with a quasi-zero stiffness section

Abstract

The paper considers the vibration isolation problem of the construction and road vehicles operator’s seat with prescribed sinusoidal displacements of the seat base. This problem is highly relevant, since the road construction vehicles operation with soil, loads, road surfaces, etc. is accompanied by the strong vibrations. The investigation was carried out in terms of the influence of the suspension static power characteristic shape on the maximum vibration acceleration of the seat. Many antivibration mechanisms have a similar static characteristic. Currently, one of the promising directions in the development of the antivibration systems is the implementation of the systems with a quasi-zero stiffness section of the static power characteristic. Such systems are preferred to dampen the low-frequency vibrations. In this paper, we study the systems having a three-segment static characteristic, which middle segment is a horizontal straight line corresponding to a section of quasi-zero stiffness. However, two extreme segments providing the braking and stopping of the mechanism when going beyond the boundaries of the quasi-zero stiffness section were described by Hermite splines with a maximum second-order derivative. The analytical expression of such a two-point spline makes it possible to set not only the function values at two boundary points, but also the values of the first two derivatives of this function at the same points, i.e. to vary the shape of such spline within a wide range. This has made it possible to consider several dozen combinations of such splines having different values of the first derivative at both boundary points, i.e. to study the differently shaped static power characteristics of the antivibration mechanism of the seat under the same sinusoidal influences. The sum of accelerations calculated for a sample of the specified seat base vibrations from the amplitude and time values combinations was used as the assessment and evaluation criterion of various static power characteristics. Furthermore, the amplitude and time values combinations, at which the maximum value of the antivibration mechanism displacements exceeded the limits of at least one of the static characteristics, were excluded from consideration and were not taken into account when calculating the criterion values. The criterion minimum value was found out to be reached at zero value of the first force derivative at the internal boundary points of the external characteristic segments, at the maximum value of the first force derivative at the external boundary points of the external characteristic segments. In this case, the first force derivative has no discontinuities on the entire static force characteristic curve. The given static characteristic is optimal according to the accepted criterion. The value of the acceleration sum criterion can be decreased fourfold in the studied range of the first derivatives from zero to twenty thousand Newton/meter.