Multi-physics Modeling of Technological Systems

6Mechanical and Electromechanical Power Transmissions

Summary

This chapter is an introduction to variational principles applied to the modeling of mechanical and electromechanical transmissions. First of all, it shows how the main concepts of system modeling, introduced in Chapter 2, can be represented using theorems that involve mechanical works and energies. These approaches facilitate the modeling of devices that have no obvious localization or decomposition of effects or the determination of the values of parameters for multi-domain devices such as the actuators. Piezoelectric transducers are used as examples of applications and illustrations of various approaches: the principle of virtual work, the energy or co-energy balances, and Lagrange equations. The exercises and problems illustrate the use of these theorems in other mechanical and electromechanical applications.

Learning outcomes

On completing this chapter, the reader is expected to:

• – Model the mechanical power transmissions without losses using an energy balance or the principle of virtual works;
• – Determine the differential-algebraic equations and the lumped parameters from an energy or co-energy balance or Lagrange equations;
• – Calculate an equivalent lumped parameter based on local expressions of elastic, electrostatic, or magnetic energies or based on finite-element simulations.

6.1. Introduction

6.1.1. Objective

The previous chapters have aimed to determine the types of effects and the forms of models ...