Active vibration control using mechanical and electrical analogies

A Torres-Perez,A Hassan,S Kaczmarczyk,P Picton

doi:10.1088/1742-6596/721/1/012013

A Torres-Perez, A Hassan + Show 2 more

Open Access

https://doi.org/10.1088/1742-6596/721/1/012013

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Abstract

Mechanical-electrical analogous circuit models are widely used in electromechanical system design as they represent the function of a coupled electrical and mechanical system using an equivalent electrical system. This research uses electrical circuits to establish a discussion of simple active vibration control principles using two scenarios: an active vibration isolation system and an active dynamic vibration absorber (DVA) using a voice coil motor (VCM) actuator. Active control laws such as gain scheduling are intuitively explained using circuit analysis techniques. Active vibration control approaches are typically constraint by electrical power requirements. The electrical analogous is a fast approach for specifying power requirements on the experimental test platform which is based on a vibration shaker that provides the based excitation required for the single Degree- of-Freedom (1DoF) vibration model under study.

Highlights

Dynamic Vibration Absorbers (DVAs) were patented by Herman Frahzm in 1909 [1] and the principles of passive DVAs design were fully described by Ormondroyd and Den Hartog [2, 3].DVAs has been extensively studied in building structures, as defence mechanism against earthquakes, to counter seismic movements and wind forces [4]
Fitting transmissibility plots to experimental results using the theoretical model in Equation 15 shows that the best damping factor is 6.1 N/(m/s) when the test was performed with an open circuit across voice coil motor (VCM) terminals and the damping factor is 20.2 N/(m/s) when a short circuit is placed across VCM terminals, Figures 12-13
Coupled mechanical-electrical systems could be analysed with electromechanical analogous circuit models

Summary

Introduction

Dynamic Vibration Absorbers (DVAs) were patented by Herman Frahzm in 1909 [1] and the principles of passive DVAs design were fully described by Ormondroyd and Den Hartog [2, 3]. Coupled electrical and mechanical systems are typically analysed using equivalent circuit models. This study analyses an active DVA and an active vibration isolation system using electrical analogous circuit models. The differential equation that describes the motion of the mass ‘m’ using 2nd Newton’s law is shown in Equation 1. Where x2 is the base excitation which is provided by the shaker table , x1 describes the spring suspended mass motion, k is the helical spring stiffness, c is the mechanical damping and U is a generic actuator force. 2.1 Equivalent circuit representation of the 1DoF active control rig with a generic actuator. A circuit analysis using Kirchoff’s Laws yields the same differential equation as shown in Equation 1. For Type I, the differential equations are obtained using KCL in node A as shown in Equation 2 and for Type II, they are obtained using KVL in loop I as shown in Equation 3

L x1 x2 dt u

Equivalent circuit representation of the 1DoF active control rig with a VCM

Electrical impedance and power requirements

Mass on the spring motion using the equivalent circuit

Model validation

Conclusion