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"The principle cannot fail. It is as powerful when applied to the earth as it is when applied to a [violin note shattering a] wineglass, a [boy pushing a man on a] swing, or a steel link. Anyone who doubts should only bear in mind the illustration of the swing. A small boy, by each time adding a pound to the force with which a 200-pound man swings, can soon set the man swinging with the force of 500 pounds. It is necessary only to keep adding a little force at the right time." Nikola Tesla – the master of resonance.
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Every object depending on its mass and stiffness when excited vibrates at its natural frequency. Watches, musical instruments, microwave ovens, mobile phones and many other devices in our day-to-day life make use of this phenomenon. However, there is an undesirable side to these vibrations that can lead to the failure of structures and components. This failure mode, resonance failures, is equally applicable to large structures and small machine parts alike. Not only bridges, towers and skyscrapers, but also blades, bearings, piping and fasteners can fail due to resonance. Air and gas vapor columns can also resonate at their natural frequencies, in the same way that percussion instruments work, and this can lead to failures.
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The war cries and the pounding of foot of marauding armies in history aimed at the destruction of the enemy’s defenses by the principle of resonance. The Biblical myth of the Fall of the Walls of Jericho (Joshua 6:3-5) seems to assert this fact.
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Large towers and buildings swaying during an earthquake can fail if the swaying coincides with the natural frequency of the structure. Architects consider this while designing these buildings. The Taipei 101, one the tallest building in the world, has a 660 Ton pendulum acting as mass damper to cancel any resonance.
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There are many examples of resonance failures in all the fields of engineering.
- Excitation by the acoustic frequency of the marching soldiers led to the collapse of the Broughton suspension bridge in 1831 and the Angers Bridge in France in 1850. Failure of the Tacoma Narrows Bridge is the most documented and had a great influence on bridge designs world over.
- Resonance of the wheels to the interaction of the wind on the rotating wheels was the possible reason for the catastrophic failures of Spinenergy-Rev X bicycle wheels. Even though this was a high performance light weight Carbon fibre wheel, these failures resulted in the withdrawal of the product.
- The failure of many midrise buildings during the 1985 Mexico earthquake was due to resonance.
- Total destruction of multi bladed helicopters while on the ground is a case of resonance of the helicopter due to shocks from the landing gear known as “ground resonance."
Today design software can model and predict the natural frequency of a given object.
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The failure in most cases is not because of very high stress on the component but because of continuous reversal of stress at a nodal point. Many times, it is not the main machine part that fails but a small attachment or fixture that fails that leads to a snowballing effect.
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Power Plant Failures
Power plants are no stranger to these types of failures.
- I remember the failure of the blades of a variable pitch axial type FD fan in a power plant. All blades of one fan failed at approximately one hundred hours of operation. The blame game was on and was put on to construction for not removing some temporary material caught between the blades, damaging one blade and subsequently all others. After a few days, the second FD fan also failed exactly the similar way and exactly and at the same hours of operation. Designers had to come in. By means of a variable frequency vibration exciter, they found out that the natural frequency of the blades coincided with a harmonic of the speed. This resulted in resonant vibration of the blades leading to fatigue failure at the root of the blades. After replacing with new design blades, the fan has been running continuously ever since.
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- As the flue gas moves or in second pass coils, the vortex shredding creates resonance of the gas columns. The vibrations lead to the failure of the tubes.
- There are cases of Boiler Safety valve failures due to vibrations caused by the resonance of the steam column in the branch pipe on which the safety valve is mounted.
- Fatigue failure of thermowells in high pressure steam piping due to flow induced resonance is another area that designers have to consider.
- Failures of pump shafts due to resonance at critical speeds and resonance due to frequencies from Variable Frequency Drives have been reported. There are cases of the pump base plate resonance that led to piping vibration and failure.
- Sub-synchronous resonance created due to the installation of series capacitors in the transmission lines led to failure of turbine shafts in the Mohave power plant in the US in 1971.
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Critical Speed of a Turbine Generator
Critical Speed of the steam turbine generator is a practical aspect of resonance in the power plant. The turbine rotor is a simply supported shaft and has a natural frequency that in terms of speed of rotation is known as the the critical speed. This is true for any rotating machine.
In a typical subcritical 600 MW 50 HZ steam turbine generator, with a normal opearting speed of 3000 rpm, critical speeds occur at 740 rpm and 2044 rpm. The different horizontal and vertical stiffness of the bearing and supports causes these two critical speeds. The operator when starting the turbine is cautious on passing this speed as quickly as possible, the “critical speed avoidance." Any unbalance in the rotor will lead to very high vibrations at the critical speeds. Any dwell time to allow for casing expansion is at speeds below or above this. Very high vibration levels when the turbines operate at these speeds can lead to catastrophic failures. You can see the Critical Speeds on the name plate of the turbine. Some turbine designs are such that the critical speeds are near the operating speeds. These turbines exhibit continuous high vibration during operation.
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Natural Frequency Resonance may be the culprit in many of the unidentified and mysterious industrial failures. When analysing failures keep in mind this possibility.