Here is the second installment on our turbine blade analysis discussion. (Part one is here: Turbine Blade Modal Analysis)

This time I will focus on a dynamic stress analysis. Once you have created the interference diagram that was discussed in my last post, you will be able to identify conditions where resonance may occur. Typically I find any case where the resonant condition is less than 3% different from the forcing frequency (impulse line on interference diagram). I then run a dynamic stress analysis on each of those conditions using BLADE.

Resonant conditions were covered in my last post, but I think it is important enough to summarize it here. The dynamic amplitude and stress response of a structure depends on the following factors:

This time I will focus on a dynamic stress analysis. Once you have created the interference diagram that was discussed in my last post, you will be able to identify conditions where resonance may occur. Typically I find any case where the resonant condition is less than 3% different from the forcing frequency (impulse line on interference diagram). I then run a dynamic stress analysis on each of those conditions using BLADE.

Resonant conditions were covered in my last post, but I think it is important enough to summarize it here. The dynamic amplitude and stress response of a structure depends on the following factors:

1. The natural frequencies of the system

2. The damping properties

3. The forcing amplitudes or stimulus ratio, defined as the ratio of the dynamic forces to the static steam loads on the blade

4. The phase angles, defined by the harmonic content (nodal diameter) of the modes.

The steam flow field is non-uniform due to nozzle asymmetry and irregular spacing geometry within the steam flow path. Other factors may include geometry variations of wakes, leakage flows and disturbances in the turbine structure such as joints and steam extractions. Since so many variables are involved and some of the fluid phenomena are still unknown, it is extremely difficult to estimate accurately the dynamic forces and consequently the stimulus ratio.

When calculating the alternating stresses using BLADE, I typically assume a 1% stimulus ratio so that results can be easily scaled. In practice the stimulus ratio varies for different machines and for different blade rows. When BLADE calculates these stresses it assumes that the system is at a resonant condition. Therefore, the resonant stresses that are output by BLADE need to be detuned (i.e. reduced) if the particular stimulus is not precisely at resonant frequency. For example let’s say the conditions that were selected to run a dynamic analysis on were within 1% of resonance and this occurs at 3500 Hz. This could lead to a significant detuning since the forcing frequency would be 35 Hz away from resonance.

The detuning of these resonant stresses is accomplished through the transmissibility function or sometimes referred to as the magnification factor. A derivation of the transmissibility function can be found in a mechanical vibrations text typically in the harmonic vibration chapter. For convenience here is the final result:

Where:

s_{d}= Dynamic Stress

s_{r}= Resonant Stress

h=Frequency Ratio (excitation frequency/natural frequency)

z =Critical damping ratio

Once the stress values are detuned you will now know the frequency and nodal diameter for each possible resonant condition and the dynamic stresses that occur there. With this you will be able to judge if this near resonant condition is significant and if a design needs to be modified to reduce the stresses or shift the frequencies to detune the resonant condition.

Thanks for reading and welcome your comments and suggestions.

Thank you for the good article. Would you please explain how do you understand bladed-disc assembly modes. How you may address a excitation mode (in-phase & resonant)has enough energy to cause significant dynamic stress of concern. For example if there is a excitation mode satisfying phase and frequency at 23rd mode, shall it be concerning? as it may not have sufficient energy to cause any problem. How to prove it?!

ReplyDelete2nd question is for partial admission stages how you may consider nozzle passing frequency. How do you account the blank arc into loading of NPF? If you have got 3 steam throttle valve at inlet where the third valve (middle one)is the margin or max. load but all 3 valves covering only portion of full first stage disc for example you can say the arcs of nozzles as follows:

1. 135 degree nozzle arc

2. 35 degree third valve not opened in design condition.

3. 135 degree nozzles arc

4. 55 degree blanked arc

In this case how the nozzle passing frequency and shock load due to change over between arcs shall be studied?

Sorry for my long list of questions.

Thank you and best regards,

Sina

Sina, I am currently working on my next post that will answer your first question on how to determine if a particular resonant condition has enough energy to cause a problem. In short you can use fracture mechanics to determine if the dynamic and steady stress is large enough to drive a crack in a blade.

ReplyDeleteAs to the partial arc admission, it is something I am currently researching myself. Some of my colleagues here at SimuTech have an immense amount of experience in this field and I will be tapping into their knowledge as soon as time permits. I think that would be a good topic for a future post.