Shafting torsional vibrations


Shafting torsional vibrations are characterized by variable speeds of shafting rotation.
Shafting torsional vibrations are characterized by variable speeds of shafting rotation. In contrast to other easily detectable types of vibration, like axial or lateral vibrations, shafting torsional vibrations are "invisible." However, this kind of shafting vibration may become, under certain circumstances, the cause of serious damages including shafting fractures.


The origin

Torsional vibrations are the characteristic of nearly all rotational machines and devices. However, torsional vibrations of internal combustion engines and their shafting are especially significant. These vibrations appear as the result of the variable revolution of rotating parts, invisible to the human eye.

The main sources:
- gas pressure;
- crank mechanism; and
- propeller.
Torsional vibrations are the consequence of a number of processes. The most common are:
  • Variable gas pressure in the cylinder of an engine;
  • Inertial forces of a crank mechanism; and
  • Fluctuation of sea water flow around the propeller.

The excitation of torsional vibrations is significantly determined by the piston's stroke and the mean effective pressure. The ongoing increase of these characteristics is the cause of increased vibration excitation in the recent propulsion plants.


Figure 1. Excitation torque on a crank pin

Figure 1.   Excitation torque generated in cylinder of a typical low-speed diesel engine during crankshaft's full revolution (360 degrees). The resultant excitation combines the influences of the gas pressure and the crank mechanism inertial forces.


Shaft load includes a variable torque component, as well as a static torque component.
The total engine excitation is the result of simultaneous action of all cylinders.
During a misfiring operation, a strong counter torque occurs.
Figure 1. shows the variation of the excitation torque on the crank pin of a typical low-speed, two-stroke diesel engine. The crankshaft load includes, besides the variable torque component, a static torque component that depends on the power transmitted and the engine speed.

Since propulsion engines are composed of a number of cylinders, the total torque is the result of the simultaneous actions of all cylinders, taking into account the phase angle between them due to the firing order, as seen in Figure 2.


Figure 2. Engine excitation

Figure 2.   Cumulative excitation torque generated in a typical five-cylinder, low-speed diesel engine during crankshaft's full revolution (360 degrees). The blue line represents the case when all cylinders work properly (normal operation). The red line represents the case when cylinder No. 3 lacks ignition (misfiring operation).

The variable torque initiates vibration of the propulsion plant components.
The variable torque, generated in the engine's cylinder, is transmitted through the shafting up to the propeller. This torque initiates the vibration movement of the propulsion plant components.

The response of a system

Mechanical systems, as a whole, possess some vibration properties denoted as natural frequencies and corresponding modes of vibration.

Resonance: the event when excitation frequency is equal to the system's natural frequency.
If the frequency of excitation, expressed as the number of impulses per second, is sufficiently different from the system's natural frequency, the system will vibrate "moderately." If, however, the frequency of excitation is equal or nearly equal to the system's natural frequency, the system will respond by strong, even severe vibrations, shown in Figure 3 below.


Figure 3. Torque variation

Figure 3.   Typical vibration torque variation in a propeller shaft of a conventional, low-speed diesel engine propulsion plant. The blue line corresponds with the system's out-of-resonance running condition, while the red line corresponds to the system's resonance running condition.


The propulsion plant, composed of the propulsion engine, the shafting and the propeller, denotes a vibration system. This system, determined by the inertia of its components, as well as by the stiffness between them, possesses its own natural frequencies and corresponding modes of vibration.

The propulsion shafting, composed of the crankshaft, the intermediate shaft and the propeller shaft, will vibrate when excited by variable torque.

The total torsional stress is a sum of the static and the vibration stress.
The main consequence of propulsion shafting torsional vibration is the occurrence of torsional vibration stresses in the components of the system (Figure 4). The total torsional stress in each component of a shafting system is then determined as the sum of a vibration stress component and a static stress component. As mentioned earlier, the static stress component is a product of power transmission.


The static stress component is not included herein.
Figure 4. Normal operation

Figure 4.   Typical torsional vibration stress response for intermediate shaft during normal operation of a conventional low-speed diesel engine propulsion plant. Stress limits for engine's continuous and transient running are also included.

The stress limits depend on many factors, including the engine speed.

Stress limits

Classification societies prescribe the amount of allowable torsional vibration stresses for engine crankshafts, intermediate shafts and propeller shafts. These stress limits are determined by the purpose, shape, material selected, dimensions and intended operation of shafting. Moreover, the stress limits are not constant; instead, they are a function of engine speed.

At the engine's low speeds, the stress limits increase, whereas at the engine's high speeds, the stress limits decrease. When the engine's speed rises, the static stress component also rises, and it is necessary that the total stress level remain within acceptable limits.

For each shaft type, there exist two distinct stress limits.
The higher stress limit should not be exceeded in any case!
For each shaft type, classification societies prescribe two values of stress limits - the lower and the higher (Figure 4).
  • The lower stress limit is applicable to the entire speed range of a propulsion plant. This limit determines the maximum stress level allowed for the continuous engine operation.
  • The higher stress limit is applicable only for a fraction of the entire speed range, i.e., up to 80% of the engine's maximum continuous speed. This stress limit represents the stress level which, in any case, should not be exceeded.
If the lower stress limit is exceeded, the barred speed range is introduced.
In the event that actual vibration stresses exceed the lower stress limit, but not the higher stress limit, the so-called barred speed range is introduced.

The barred speed range must be passed through rapidly. Actually, torsional vibrations need some time to fully develop and, if the barred speed range is passed sufficiently rapidly, there is a great possibility that the full stress level will never be reached.

The barred speed range is clearly noted in red on the tachometer, as well as on notice boards. Moreover, more recent propulsion plants are equipped with special devices that ensure that this range is rapidly passed.

The intermediate shaft vibratory stress variation, as shown in Figure 4, exhibits some interesting points deserving of more clarification.

  • Engine speed ranges below 40 rpm and over 70 rpm are characterized by moderate, even low stress levels. Torsional vibration stress is exceptionally low in the engine speed range above 90 rpm, i.e., in the vicinity of an engine service speed that is 105 rpm. Fortunately, the static torsional stress component is the largest in this region.
  • The peak vibration stress is reached at 55 rpm, when the engine output is less than 15% of the maximum continuous rating. At the same time, the static stress component amounts to approximately one third of the shaft static stress at the nominal engine speed. This is due to the resonance between the excitation torque and the system's natural frequency. Therefore, this engine speed is usually called the critical speed.
  • In the engine speed range between 53 and 57 rpm, the actual vibration stress is higher than the stress limit for continuous running, and the barred speed range is introduced. For the safety reasons, the actual restricted speed range is usually imposed in a slightly wider interval.


The influence of one cylinder not firing

Each kind of firing irregularity increases vibratory stresses.
One cylinder not firing is an extreme kind of firing irregularity.
In general, any irregularity in cylinder firings usually produces enlarged vibratory stresses in the components of a propulsion plant. As shown in Figure 5, the absence of firing in one of the cylinders significantly changes entire propulsion plant torsional vibration behavior.


Figure 5. Misfiring

Figure 5.   Typical torsional vibration stress response for intermediate shaft during one cylinder misfiring operation of a conventional, low-speed diesel engine propulsion plant. Stress limits for the engine's continuous, as well as transient running are also included.

Misfiring in any one cylinder causes the rise of resonances that are small, even negligible, during the engine's normal operation. Moreover, these resonances are usually placed in the vicinity of an engine's rated speed and thus cause an additional operation limitation. Fortunately, these operation limitations are not permanent, but only applicable until the resolution of the problem.

No barred speed ranges are allowed in the region above 80% of the rated speed.
Peaks on a diagram correspond to system resonances.
In the case of an intermediate shaft, as shown in Figure 5, the additional speed restrictions would be, together with the previous case, in the interval between 80 rpm and 86 rpm, as well as in the region above 102 rpm. Since no one classification society allows barred speed ranges in the region above 80% of the rated speed, the operation limitation will read: "In the event of one cylinder misfiring, the maximum engine speed is not to exceed 80 rpm." The note of this or a similar meaning should be included in the propulsion plant operation manual.


More on resonance

The resonance is a state of movement when the system vibrates in phase with an externally applied load.


Figure 6. Resonances

Figure 6.   Resonances


The excitation torque is composed of a number of single harmonic excitations.
Each single harmonic excitation has its own frequency.
The system response is also constructed from a number of single harmonic responses.
The excitation torque is composed of a number of single harmonic excitations. Each single harmonic excitation has its own frequency, which is a multiple of the shaft rotation frequency. This multiple is called the order. There exists the first order excitation, the second order excitation, etc. Of course, the n-th order excitation produces the n-th order response. Finally, the system response, shown in Figure 6, is also constructed from a number of single harmonic responses.

Each single harmonic response has its own system resonance. Various peaks on the diagram in Figure 6 correspond to such system resonances.

The main resonance, usually denoted as a system main critical speed, occurs when the system vibrates in phase with the n-th order excitation. If the propulsion plant is powered by a two-stroke engine, n is equal to the number of engine cylinders. If, on the other hand, the propulsion plant is powered by a four-stroke engine, n is equal to the one half of the number of engine cylinders.


Counteracting shafting torsional vibrations

The most effective countermeasure is an appropriate shafting design.
It is extremely important to act as soon as possible.
Later, the possible solutions are rare and expensive.
The easiest, fastest and most cost-effective way to counteract shafting torsional vibrations is in the propulsion shafting design phase. Later, when the propulsion shafting is finished and put in operation, satisfactory solutions are rare and more expensive.

During the propulsion shafting design phase, it is possible by proper design to keep vibration responses within the allowable limits. The most usual measures are:

  • selection of appropriate dimensions and materials,
  • selection of appropriate turning wheel,
  • selection of appropriate tuning wheel, and
  • selection of engine appropriate location, if applicable.

Minor torsional vibration problems of an existing propulsion plant may be resolved by appropriate operations, i.e., by the rapid pass through the hazardous speed ranges. If this is not applicable, the only possible solutions are the propulsion shafting redesign, or mounting of a torsional vibration damper.

The torsional vibration damper is a device that should be mounted on the fore end crankshaft flanges. It absorbs some vibration energy from the system and in that way saves the propulsion shafting components from the unacceptable stress levels. However, it should be clearly realized that this solution may be prohibitively costly - the cost of a large torsional vibration damper may be in excess of 100,000 USD per piece.

   


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