Page 322 - The Mechatronics Handbook

15

The Physical Basis

of Analogies in Physical

System Models

15.1 Introduction
15.2 History
15.3 The Force-Current Analogy: Across
and Through Variables
Drawbacks of the Across-Through
Classification • Measurement as a Basis
for Analogies • Beyond One-Dimensional
Mechanical Systems • Physical Intuition
15.4 Maxwell’s Force-Voltage Analogy:
Effort and Flow Variables
Systems of Particles • Physical Intuition • Dependence
on Reference Frames
Neville Hogan
15.5 A Thermodynamic Basis for Analogies
Massachusetts Institute Extensive and Intensive Variables • Equilibrium and
of Technology
Steady State • Analogies, Not Identities • Nodicity
Peter C. Breedveld 15.6 Graphical Representations
University of Twente 15.7 Concluding Remarks

15.1 Introduction

One of the fascinating aspects of mechatronic systems is that their function depends on interactions
between electrical and mechanical behavior and often magnetic, fluid, thermal, chemical, or other effects
as well. At the same time, this can present a challenge as these phenomena are normally associated with
different disciplines of engineering and physics. One useful approach to this multidisciplinary or “multi-
physics” problem is to establish analogies between behavior in different domains—for example, resonance
due to interaction between inertia and elasticity in a mechanical system is analogous to resonance due to
interaction between capacitance and inductance in an electrical circuit. Analogies can provide valuable
insight about how a design works, identify equivalent ways a particular function might be achieved, and
facilitate detailed quantitative analysis. They are especially useful in studying dynamic behavior, which
often arises from interactions between domains; for example, even in the absence of elastic effects, a mass
moving in a magnetic field may exhibit resonant oscillation. However, there are many ways that analogies
may be established and, unfortunately, the most appropriate analogy between electrical circuits, mechan-
ical and fluid systems remains unresolved: is force like current, or is force more like voltage? In this
contribution we examine the physical basis of the analogies in common use and how they may be extended
beyond mechanical and electrical systems.

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