Understanding the basic factors of the machinery vibrational behaviour goes beyond machinery dynamic modelling.
It should involve deep understanding of the machinery's dynamic behaviour during its operation and in any malfunction situation.
Machinery vibration monitoring requires appropriately selected and strategically located vibrational sensors for capturing the machinery vibration. The target of this article is to set out clearly and concisely the impacts of a cracked shaft on the machinery vibrations.
Vibration monitoring as a critical part of predictive maintenance programs assists in achieving smooth and long-term operation and has proven to be highly cost effective.
The cracked rotating component diagnostics using vibration data combined with operational data is discussed. The advantages of vibration monitoring method as a powerful diagnostic tool are emphasised.
A crack initiation could be because of many mechanical or thermal reasons. Subsequently, the crack growth could be driven by a combination of thermal and mechanical loads, particularly those causing alternate cyclic stress in the shaft.
A crack is likely to be influenced by the various mechanical stresses (particularly bending stresses), the thermal fields and by fluid pressure in the cracked area.
High thermal stresses arise in geometric transition zone for many turbomachines. Thermal fatigue is cause of many crack initiation incidences. Some cracks originate from surface micro-cracks (this could be result of many manufacturing and operational reasons).
On the shaft surface (where the shaft or sleeve is in contact with the fluid), maximum stress could be expected because of the maximum thermal gradient and/or the maximum bending effect. Even if a shaft sleeve is used, a high stress could occur on the shaft surface.
[Image alongside depicts an example of a crack in a turbomachine shaft.]
The location of the thermal boundary zone in a shaft is critical. If the thermal boundary is located above the crack, tensile stresses that develop in correspondence with the crack could facilitate its opening. If the thermal boundary is below the crack, compressive stresses arise and this force could attempt to close the crack.
The thermal stresses and bending stresses are usually responsible for the micro-crack generation, the crack initiation and the propagation of the crack.
Generally, the thermal load, the bending stresses, the axial load, the mass unbalances, and the fluid pressure entering between two crack faces can generate a stress distribution within the shaft and aid the propagation of a crack.
The influence of the axial force would keep the crack open and the fluid pressure on the crack faces would act in the same way.
Crack detection
A propagating crack generally produces a bow, which can be magnified by mechanical/thermal stresses and by the fluid pressure penetrating between the two crack faces.
The bow could generate high amplitude of 1× vibrations. In other words, the 1× vibration components are generated by the crack-related developing bow, as well as by the mechanical, thermal and hydraulic unbalances.
The 1× vibration component increases consistently when the unbalance is in-phase with the bow. This situation is probably the most likely to occur, since the crack usually starts from micro-cracks where the maximum stresses are developed.
The 2× analysis is usually the most convenient way to detect a crack. A cracked rotor presents two events at each rotation.
[Pictured alongside is an example of defects on an axial impeller.]
Any cracked-shaft formulation shows periodically-variable stiffness with a speed two-times the rotor speed.
An open crack generates 2× vibration components which could mainly be proportional to the depth of the crack, the bending moment and various loads (such as the fluid hydraulic forces).
A crack with a small depth would just generate a weak excitation of the 2× component. It could be difficult to detect a crack from an abnormal evolution of the 2× vibration component.
Sometimes, the 2× component is so small that it could be masked by the noises. In such cases, a crack is only recognisable with advanced filtration methods (such as a nonlinear type "Kalman Filter" analysis).
The 2× vibration amplitude can be a highly nonlinear function of the depth. For example, in a case study, only 10 to 20 percent increase in the crack depth resulted in a more than 60 percent increase in the 2× vibration amplitude.
The 2× vibration components are also proportional to the fluid radial forces. The operation of a turbomachine far from the design point can consistently increase the hydraulic load and the 2× vibration.
The combination of crack excitations and 1× excitation generates the 3× vibration. The 3× vibration component is usually smaller than the 2× vibration amplitude. However, in some special instances the 3× vibration could be at the same order or even slightly higher compared to the 2× component.
The dynamic load, stiffness, and (particularly) damping of bearing and seal could show a high sensitivity to small differences in design, manufacturing (manufacturing details and tolerances), assembly (assembling tolerances) and operational effects (such as the degradation) so that the responses of similar turbomachines can be quite different.
[Pictured alongside is an example of a complex rotor/shaft for a gas turbine.]
A theoretical prediction of exact vibration behaviour (such as vibration amplitude) of a cracked-shaft would not be suitable for crack detection.
The trending can be the best tool for this purpose.
The increases of 1×, 2× and 3× vibration measurement amplitudes from their acceptance regions (established based on the normal operating condition) can help to detect a crack.
There are many other vibration indications for a crack (monitoring).
For example, vibration measurements could be useful at transient conditions (starting and run-down transients are often too fast to allow the collection of significant data).
However, high 1×, and 2× amplitudes (compared to normal levels) are the most significant symptoms of a crack. The vibration measurements could be in position(s) rather far away from the crack.
Usually, the vibration amplitudes will increase in all locations of a shaft as a result of a crack. Most often, the vibrations in various parts of a shaft could be at least 20 percent of its maximum (located close to the excitation).
A case study is presented for a crack initiation and propagation in a centrifugal compressor shaft. In this turbo-compressor, the steady state 1× and 2× vibrations were reported around 25 micron and 6 micron, respectively.
In a 10-day period, the 1× and 2× vibrations increased to 41 micron and 10 micron, respectively (around 60 to 70 percent increase). After another 10 days (totally 20 days), the 1× and 2× vibrations reached 76 micron and 17 micron respectively (around three times of the established normal operating vibrations).
The machine tripped and the shaft was inspected. The high vibration was because of a propagating crack on the shaft.
Vibration monitoring is one of most effective and powerful modern condition monitoring methods. It enhances efficiency, reliability, availability, and safety of rotating machines.
It reduces production losses. Synchronous and non-synchronous vibration studies (such as 1×, 2×, 3× and others) are used for identification of basic dynamic characteristics of rotors.
Amin Almasi is lead rotating equipment engineer at WorleyParsons Services in Brisbane. He specialises in rotating machines including centrifugal, screw and reciprocating compressors, gas and steam turbines, pumps, condition monitoring and reliability.