A modeling concept of a mechanical system having a piecewise linear spring property for its diagnosis

Abstract

Machine condition monitoring and fault diagnosis of rotating machinery are very important because of the wide use of rotating machinery in industry. Couplings and gears are used in many mechanical sys tems to connect elements and transmit power. The system is usually modeled as a single degree of free dom system with a piecewise linear spring property, where the mass of main machine is only considered. In the present study, the dynamic behavior of a system with an unsymmetrical nonlinearity and a signif icant mass of the connecting part was investigated both experimentally and by numerical simulation. In the experiment, a 1/3 sub harmonic oscillation was observed, but this oscillation was not found in the simulation using a single degree of freedom system, in which the mass of the connecting part was ignored. However, when a two degrees of freedom system was used that considered both the mass of the connecting part and the impact property, the 1/3 sub harmonic oscillation was observed. Thus it is recognized that an adequate mathematical model for diagnosis in the early stage of abnormality must be selected on the basis of the mass ratio between the connecting part and the main body.

Natural frequencies of a cantilever beam and block system with clearance while block staying on given position

“…The solid-to-solid contact stiffness and the stiffness of the contact gap are denoted as ks,kc, respectively. By using a piecewise linear spring model used by Kawamura et al (2009), there can be three force conditions: where cs is the damping coefficient during the process of solid-to-solid contact, and ur=um-ub.…”

“…Karlberg (2010) derived the analytical expressions for the approximated pedestal stiffness for rotating machinery supported by bearings with radial clearance, and found that frequencies of the system decreased significantly with clearance. Kawamura et al (2009) employed a kind of piecewise linear spring, e.g. soft spring and hard spring, to model the flexible coupling and shaft with clearance.…”

Fundamental study on countermeasures against subharmonic vibration of order 1/2 in automatic transmissions for cars

“…In previous studies, we analytically clarified the mechanism that produces subharmonic vibration in automatic transmissions and performed experiments and MATEC Web of Conferences 211, 13004 (2018) https://doi.org/10.1051/matecconf/201821113004 VETOMAC XIV numerical analyses using a simple one-degree-of-freedom system with the piecewise-linear spring [1][2][3]. Although a number of studies [4][5][6] have examined nonlinear vibrations in mechanical systems having piecewise-linear spring properties, countermeasures against the subharmonic vibration have not yet been studied. In this study, we experimentally and analytically examined a countermeasure against the subharmonic vibration by increasing the stages of the piecewise-linear spring using the one-degree-of-freedom system model.…”

Effect of Stiffness Ratio of Piecewise-Linear Spring on the Occurrence of Subharmonic Nonlinear Vibration in Automatic Transmission Powertrain

“…Although a number of studies [1,2,3] have examined nonlinear vibrations in mechanical systems having piecewise-linear spring properties, these studies are not related to forced vibration analysis using a piecewise-linear spring applied in an actual torque converter of a passenger car. The authors clarified the occurrence mechanism of the subharmonic vibration of order 1/2 [4].…”