Vibrations of a rigid body with a controlled frictional electromagnetic seismic damper: nonlinear model

Abstract

A nonlinear mathematical model of a gravitational vibratory system with a controlled electromagnetic seismic damper is developed. The dependence of the force of attraction of ferromagnetic bodies by the solenoid of the frictional device on the solenoid current is established for a specific solenoid design. The analytic expression for this force is derived by the least-squares method using a system of continuous piecewise-linear functions. It is used to describe the pressure of the solenoid on the friction surface. For multifrequency inertial excitation, the acceleration amplification factor is evaluated depending on the time constant and gain for two cases of control. The possibility of damping vibrations by controlling the absolute velocity and acceleration is established Keywords: gravitational vibratory system, electromagnetic seismic damper, nonlinear model, feedback circuit, least-squares method, multifrequency inertial excitation Introduction. Seismic isolation mechanisms (SIMs) have been used for earthquake protection since the second half of the 20th century [5,6,11,[14][15][16][17][20][21][22][23]. Such mechanisms are designed to weaken the coupling between protected structures and ground and to dissipate the energy of seismic disturbances. Controlled semiactive seismic dampers have come to be used in recent decades [13][14][15][16][17]22]. Semiactive control systems fall into the class of systems in which control is used to change the physical and mechanical properties of shock-absorbing elements of damping devices. Such devices may include electro-and magnetorheological liquid materials whose parameters are strongly dependent on the electric and magnetic fields applied to them. Such controlled devices are quite difficult to manufacture and operate. However, controlled damping can easily be produced by using assemblies with controlled pressure between frictional elements that contain solenoids with ferromagnetic cores, and there is no need for any liquid rheological materials. The cores slide over ferromagnetic surfaces, overcoming the Coulomb force proportional to the contact pressure and dependent on the ampere-turns of the solenoid [3]. To determine the contact force of attraction between arbitrary electromagnets, use is made of a theoretical-and-experimental method for each design of electromagnetic damping device.Here we use a theoretic-and-experimental method to find the contact force of interaction between a solenoid core and a ferromagnetic body. We will model the forced vibrations of a system with a controlled electromagnetic frictional damper of a one-degree-of-freedom object for two different control laws for the solenoid current.

Dynamics of vibration isolation system with a quasi-isochronous roller shock absorber

“…This kinematic constraint shows that the parameters R and r are limited only by the trivial condition R r , > 0. This distinguishes the brachistochrone-shaped surface from that considered in [18,[33][34][35].…”

“…(4), (5) will remain structurally invariant. A similar problem with a braked roller and spherical working surfaces was addressed in [18,[33][34][35].…”

Nonlinear dynamics of a system of rigid bodies with controlled electromagnetic dampers

“…For numerical integration of such systems, the step of integration should be selected considering that the system includes fast variables. Numerical integration was conducted in [8] to analyze the effect of the lag in the control loop on the resonant characteristics of a one-mass system with the magnet current controlled by speed and acceleration. In the limiting case where the parameter T j is very small, it is possible to assume that T j = 0.…”

“…A possible way to improve the dissipative properties of seismic-protection devices is to use frictional electromagnetic dampers without magnetorheological suspensions. Such a damping mechanism for a one-mass system is described in [8,11].In this paper, we model a multimass system of bodies with such a damper in the seismic-isolation mechanism. The SIM includes ball supports and built-in electromagnetic frictional elements, which generate a force resisting the motion of the SIM platform depending on the magnet current.…”

“…A possible way to improve the dissipative properties of seismic-protection devices is to use frictional electromagnetic dampers without magnetorheological suspensions. Such a damping mechanism for a one-mass system is described in [8,11].…”