DYNAMICS IN BLADE

The excitation of any blade comes from different sources. They are: a) Nozzle-pa ssing excitation: As the blades pass the nozzles of the stage, they encounter fl ow disturbances due to the pressure variations across the guide blade passage. T hey also encounter disturbances due to the wakes and eddies in the flow path. Th ese are sufficient to cause excitation in the moving blades. The excitation gets repeated at every pitch of the blade. This is called nozzle-passing frequency e xcitation. The order of this frequency = no. of guide blades x speed of the mach ine. Multiples of this frequency are considered for checking for resonance.

b) Excitation due to non-uniformities in guide-blades around the periphery. Thes e can occur due to manufacturing inaccuracies, like pitch errors, setting angle variations, inlet and outlet edge variations, etc.

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For HP blades, due to the thick and cylindrical cross-sections and short blade h eights, the natural frequencies are very high. Nozzle-passing frequencies are th erefore necessarily considered, since resonance with the lower natural frequenci es occurs only with these orders of excitation. In LP blades, since the blades a re thin and long, the natural frequencies are low. The excitation frequencies to be considered are therefore the first few multiples of speed, since the nozzle-passing frequencies only give resonance with very high modes, where the vibratio n stresses are low.

The HP moving blades experience relatively low vibration amplitudes due to their thicker sections and shorter heights. They also have integral shrouds. These sh rouds of adjacent blades butt against each other forming a continuous ring. This ring serves two purposes – it acts as a steam seal, and it acts as a damper for t he vibrations. When vibrations occur, the vibration energy is dissipated as fric tion between shrouds of adjacent blades.

For HP guide blades of Wesel design, the shroud is not integral, but a shroud ba nd is riveted to a number of guide blades together. The function of this shroud band is mainly to seat the steam. In some designs HP guide blades may have integ ral shrouds like moving blades. The primary function remains steam sealing.

In industrial turbines, in LP blades, the resonant vibrations have high amplitud es due to the thin sections of the blades, and the large lengths. It may also no t always be possible to avoid resonance at all operating conditions. This is bec ause of two reasons. Firstly, the LP blades are standardized for certain ranges of speeds, and turbines may be selected to operate anywhere in the speed range.

The entire design range of operating speed of the LP blades cannot be outside th e resonance range. It is, of course, possible to design a new LP blade for each application, but this involves a lot of design efforts and manufacturing cycle t ime. However, with the present-day computer packages and manufacturing methods, it has become feasible to do so. Secondly, the driven machine may be a variable speed machine like a compressor or a boiler-feed-pump. In this case

also, it is not possible to avoid resonance. In such cases, where it is not poss ible to avoid resonance, a damping element is to be used in the LP blades to red uce the dynamic stresses, so that the blades can operate continuously under reso nance also. There may be blades which are not adequately damped due to manufactu ring inaccuracies. The need for a damping element is therefore eliminated. In ca se the frequencies of the blades tend towards resonance due to manufacturing ina ccuracies, tuning is to be done on the blades to correct the frequency. This tun ing is done by grinding off material at the tip (which reduces the inertia more than the stiffness) to increase the frequency, and by grinding off material at t he base of the profile (which reduces the stiffness more than the inertia) to re duce the natural frequency.

The damping in any blade can be of any of the following types: a) Material dampi ng: This type of damping is because of the inherent damping properties of the ma terial which makes up the component. b) Aerodynamic damping: This is due to the damping of the fluid which surrounds the component in operation. c) Friction dam ping: This is due to the rubbing friction between the component under considerat ion with any other object. Out of these damping mechanisms, the material and aer odynamic types of damping are very small in magnitude. Friction damping is enorm ous as compared to the other two types of damping. Because of this reason, the d amping elements in blades generally incorporate a feature by which the vibration al energy is dissipated as frictional heat. The frictional damping has a particu lar characteristic. When the frictional force between the rubbing surfaces is ve ry small as compared to the excitation force, the surfaces slip, resulting in fr iction damping. However, when the excitation force is small when compared to the frictional force, the surfaces do not slip, resulting in locking of the surface s. This condition gives zero friction damping, and only the material and aerodyn amic damping exists. In a periodically varying excitation force, it may frequent ly happen that the force is less than the friction force. During this phase, the damping is very

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less. At the same time, due to the locking of the rubbing surfaces, the overall stiffness increases and the natural frequency shifts drastically away from the i ndividual value. The response therefore also changes in the locked condition. Th e resonant response of a system therefore depends upon the amount of damping in the system (which is determined by the relative duration of slip and stick in th e system, i.e., the relative magnitude of excitation and friction forces) and th e natural frequency of the system (which alters between the individual values an d the locked condition value, depending upon the slip or stick condition).