Negative Stiffness and Instability

The idea of negative stiffness might appear at first glance to be counter intuitive but that is what happens often to machinery in the real world. When such a phenomenon strikes, it triggers rapid deterioration of a machinery system.

Positive stiffness is a material property that tries to resist a force when applied on to a material, i.e. it tries to push back the force.

On the other hand, negative stiffness is a property that amplifies the deformation of a material when force is applied to a body.

Since such amplification is non-linear by nature it forces the system to go far away from its equilibrium position. When it does so, the system become unstable and as deformation quickly increases, the system fails.

The best possible way to detect the sudden appearance of negative stiffness is to monitor the displacement parameter of vibration. This is because displacement is related to stiffness. When displacement increases disproportionately without a corresponding increase in velocity parameter we would know that the phenomenon is that of negative stiffness. In addition, we might also notice a variation in the displacement readings. They don’t tend to settle to a steady state.

Negative stiffness might occur in many ways. It may happen when interference or push fitted elements come loose. It often happens to elements that are deformed over time like foundation supports or are pre-stressed like anti-friction bearings. It might happen when elements are worn out by a certain extent by different wear processes like corrosion or abrasive wear.

But in all cases, a very small change induces a system with positive stiffness to flip to negative stiffness, causing catastrophic damages and failures.



For a lucid understanding of the nature of negative stiffness you may refer to this article.

For an understanding of negative stiffness and isolation you may see this.

Effect of Triplen Harmonics on Electrical Systems

Operation and Maintenance have become complex in modern plants. Energy being one of the most important components of the cost structure, effort is on to save energy as much as possible. As a result three important changes happened over the years.

First, loads have become non-linear in nature based on lean manufacturing principle of producing as much as needed as and when needed to match customer needs and expectations without incurring wastage.

Second, changes and modifications in the electrical drive systems have become a significant improvement activity. Thyristor and SCR drives of yesteryear are now being replaced by precise IGBT (Insulated Gate Bi-polar Transistor) devices. Almost all drives are now fitted or retrofitted with variable frequency drives suitable for different motor frame sizes.

Third, most plants are generating and consuming their own electricity though captive power installed in their facilities.

Though this has given us a lot of advantage it has also brought in some hidden problems. One of the disturbing problems is the growing presence of electrical harmonics that affect equipment performance and disturb smooth operation of a plant.

Whether the presence of harmonics can disturb the operation of a factory or not would depend on the ‘stiffness’ of the power distribution system and the susceptibility of the connected equipment and components like motors, bearings, solenoids, cables, couplings etc.

Harmonics are a big polluter. Such pollution is often carried back into the electric distribution system and may affect neighboring facilities. Such pollution also causes a rise in the consumption of electrical energy – the very thing we are trying to save.

The point is how to detect the presence of harmonics in the system? Vibration spectrums often fail to detect or show up the presence of such harmonics. As a result Current Spectrum Monitoring’ is being used as a preferred technique to detect the presence of harmonics. But this technique does a good job for higher rated motors – generally for motors over 900 KW.

So what do we do for other motors lesser than 900 KW?

There seems to be an easy way out. Harmonics create excessive neutral current. This results in overheated neutrals that might be easily detected by use of Infra-red thermal imaging technique applied to MCC (Motor Control Center) and PCC (Power Control Center).

But there is something very strange about these electrical harmonics.

The ‘triplen’ harmonics i.e. the 3rd, 9th and the 15th harmonics of the line frequency cause more damage to the system and heat up the neutral. Why is that?

This is because these harmonics are actually ‘additive’ (vector addition) in nature in the neutral of a 3 phase ‘wye’ circuit. This is easy to understand. In a 3 phase ‘wye’ circuit the phases are separated from one another by 120 degrees. Now if we multiply 120 by 3 or 9 or 15 we get an integer multiple of 360 degrees, which is one complete cycle. This puts the harmonics from each of the 3 phase conductors in phase with each other in the neutral. Hence the neutral heats up.

Note this would not happen with other harmonics like 2nd, 4th, etc since that would not involve all conductors of the 3 phase to be in phase with each other in the neutral. This I call the prime number effect of number 3 and combination of 3 with other primes like 3, 5, 7 etc.

Triplen harmonics also overheat transformers (especially delta – wye types), affect solenoids (used in hydraulic circuits), lightening ballasts, non-linear loads like computers and indirectly initiates premature failure of anti-friction bearings. In short it creates a random failure pattern across a manufacturing unit, which most often becomes quite puzzling.

Not only the triplen harmonics affect plant reliability but also increases the losses of electrical power since the losses in electrical power are proportional to the square of the harmonic value.

Hence it is important to detect the presence of triplen harmonics for safe and reliable operation of the plant. Fortunately, infra-red thermal imaging comes to our rescue to detect this hidden enemy of plant reliability, availability and performance.