Characterization of the Optimal Damping Coefficient in the Continuous Contact Model

This paper presents an analytical formula to characterize the damping coefficient as a function of system's parameters in a continuous force model of impact. The contact force element consists of a linear damper which is in a parallel connection to a spring with Hertz force-deformation characteristic. Unlike the existing models in which the separation condition is assumed to be at the time at which both zero penetration (deformation) and zero force occur, in this study, only zero contact force is considered as the separation condition. To ensure that the continuous contact model obtains the desired restitution, an optimization process is performed to find the equivalent damping coefficient. The analytical and numerical investigations show that the resulting damping coefficient can be expressed as a function of system's parameters such as the effective mass, penetration speed at the start of the impact, Hertz spring constant, and the coefficient of restitution.

Characterization of the Damping Coefficient in the Continuous Contact Model

This article presents an analytical formula to characterize the damping coefficient in a continuous force model of the direct central impact. The contact force element consists of a linear damper which is in a parallel connection to a spring with Hertz force-deformation characteristic. Unlike the existing models in which the separation condition is assumed to be at the time at which both zero penetration (deformation) and zero force occur, in this study, zero contact force is considered as the separation condition. To ensure that the continuous contact model obtains the desired restitution, an optimization process is performed to find the damping coefficient. The numerical investigations show that the damping coefficient can be analytically expressed as a function of system’s parameters such as the effective mass, penetration speed just before the impact, Hertz spring constant, and the coefficient of restitution.

Analysis on Motion Precision Reliability of Hydraulic Support

In order to research the motion precision reliability of hydraulic support when the influence of the bar length error and gap error is considered, the motion trace mathematical model for the top beam of hydraulic support is established, with the calculation method of motion precision reliability and the effective length of bar based on continuous contact model. Taking some type of hydraulic support as an example, its motion precision reliability is calculated and analyzed. The Monte Carlo simulation is also used to verify the model, and the T-R curve of the gap error and the reliability is plotted. The results from simulation accord with those from the theoretical calculation, which verifies the model established and can provide some valuable reference for the related future research.

Study on the Influence of the Damping to Nonlinear Vibration Caused by Pair Clearance

Because the two components have relative motion, pair clearance is inevitable. With the machine’s speed increasing, nonlinear vibration phenomenon caused by clearance is much obviously. The state of damping in pair clearance will often make mechanism’s nonlinear vibration appear different status. For the study of damping in joint clearances impact to nonlinear vibration, four-bar mechanism with clearance is taken as research object. A nonlinear dynamic model has been established based on continuous contact model. Through analysis the nonlinear vibration in different damping and clearance, it can be found that in weak damping condition, nonlinear vibration in small pair clearance is more sensitive to the small changes of damping than that in large pair clearance. So, it’s very important to keep the pair clearance in proper lubrication conditions.

CORRELATION FUNCTIONS AND INVARIANT MEASURES IN CONTINUOUS CONTACT MODEL

We study the continuous version of the contact model. Using an analytic approach, we construct the non-equilibrium contact process as a Markov process on configuration space. The construction is based on the analysis of correlation functions evolution. The problem concerning invariant measures as well as asymptotics of correlation functions are also studied.