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# Modeling Hysteresis

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Mechanics Corner

A Journal of Applied Mechanics and Mathematics by DrD, #41

(c) Machinery Dynamics Research, July 2017

Modeling Hysteresis

1. Introduction

What do you know about hysteresis? Many Mechanical Engineers will associate this term with the magnetization curve of a piece of magnetic material, and quickly conclude, "I don't have to worry about that!" But that would be wrong. While hysteresis does occur in magnetic systems, it happens in many other situations as well, many of them situations of concern to mechanical engineers.

Figure 1 Typical Hysteresis Curve

Figure 1 shows a typical hysteresis curve, and it makes no difference as to what physical phenomena are involved. The red curve is the actual hysteresis curve. The blue curve is called the "spine."

And yet, nobody has any reaction at all! At this point, almost 500 people have looked at this, but no one has any reaction at all! Is no one interested, amused, angered, puzzled, or disgusted with this post? Why are there no comments at all? I don't understand!!

DrD

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Some of actual real-life hysteresis:

1. gear hysteresis

2. material properties after reaching plastic region of tension test

I will add if I could think other cases.

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Thanks for the comment, Henry.

Actually, it is not necessary to go all the way to the plastic range to see hysteresis. In very lightly damped systems, such as an all steel machine shafting system, hysteretic damping is one of the principal damping mechanisms at work.

DrD

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As another example of hysteresis in mechanical systems, consider the anti-vibration engine mounts made by coiling wire rope into a helix. The helix is laid with the axis horizontal, and the bottom is attached to the foundation while the top is attached to the engine. As the engine vibrates, this causes the coils to flex, and the internal friction between the individual strands of the wire rope give rise to hysteretic friction.

DrD

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