Hi all,
I have the task of designing the casing of some electronics which are going to be exposed to a launch environment and so have to ensure that the casing can withstand the loads due to random and sinusoidal vibration as well as shock loading. I am a bit unclear as to how to go about doing this so I thought I'd see if anyone here can give me some advice on this.
Here is the method I've employed so far. The casing is a "cuboid" shape so I've considered it to be made from 6 rectangular panels. Using ESDU methods and by assuming each panel to behave as a simply supported plate I've calculated the resonant frequencies of each panel. Next, for the loading which the case will encounter I have been given a table of the PSD (power spectral density) versus frequency from 20Hz up to 2000Hz and so using this I know what resonance modes will be excited within the loading's frequency range. To calculate the stress which a panel will experience due to resonating at a particular frequency I've determined the RMS acceleration using the PSD value, the value of the resonant frequency and the dynamic magnification factor [ Q = 1/(2*DAMPING FACTOR) ] and multiplied this by 3 to account for maximum deviation from this RMS value. I've seen this method referred to as "Miles' Method".
From here I've used what seems sensible to me to relate this 'vibrational acceleration' to the stresses which result, I was wondering if someone could give me some input on if this is the correct approach as I basically made up this method as I went along but I think it's based on reasonably sound logic. I know the mass of the panel and the acceleration, multiplying these gives the force applied to the panels,this force should act uniformly over the panel rather than as a point load through its centre of gravity (because the entire body is vibrating) so by dividing this force by the area of the panel I can determine an equivalent pressure which would result in the same deformation/acceleration when applied over the panel's surface. Using this pressure value I used a separate ESDU source which allows for the stress in a rectangular panel due to a uniform pressure being applied to be calculated and have taken this stress value to size the thickness of the casing panels. As for the stresses in the bolts, if the bolts pass through the panels into the other sides of the casing i figure all they have to do is react the maximum load which resulted from the vibrational acceleration as this will act perpendicularly to the panel's surface so it's just F/(number of bolts) for the force which each bolt must react and then determine the stress from there and size the bolts to not fail under this stress.
For the shock loading I've done something similar: I used the maximum shock acceleration (given in loading data) multiplied by a dynamic magnification factor (I was told to use a value of Q = 2, not sure if this is correct of not for shock loading?) multiplied by the panel mass to determine the maximum force applied to the panel and then divided this force by the panel's area to find an equivalent pressure and calculated the stress due to this pressure then used this to determine the thickness required to withstand the loading. The final thickness of the panels will be the larger of the thicknesses needed to survive the shock loads and to survive the fatigue loading due to vibration.
Like I said I think this method is based on some decent engineering/physics logic and I realise that there are some simplifications made but without resorting to a finite element model is this a reasonable approach for designing the casing? Any idea how any simplifications that I've made may impact the accuracy of the results? Should this be reasonably close to the stress results which would be observed during testing or miles off? I realise that the plates won't act as simply supported so this is one such simplification. An FE model will be built later of the casing but I'd like to get a feel for the figures first and to make comparisons with the FE results later.
Any input will be much appreciated, looking forward to seeing what people think of this approach...whether they agree with it or think it's complete nonsense really!
Cheers,
Simon
I have the task of designing the casing of some electronics which are going to be exposed to a launch environment and so have to ensure that the casing can withstand the loads due to random and sinusoidal vibration as well as shock loading. I am a bit unclear as to how to go about doing this so I thought I'd see if anyone here can give me some advice on this.
Here is the method I've employed so far. The casing is a "cuboid" shape so I've considered it to be made from 6 rectangular panels. Using ESDU methods and by assuming each panel to behave as a simply supported plate I've calculated the resonant frequencies of each panel. Next, for the loading which the case will encounter I have been given a table of the PSD (power spectral density) versus frequency from 20Hz up to 2000Hz and so using this I know what resonance modes will be excited within the loading's frequency range. To calculate the stress which a panel will experience due to resonating at a particular frequency I've determined the RMS acceleration using the PSD value, the value of the resonant frequency and the dynamic magnification factor [ Q = 1/(2*DAMPING FACTOR) ] and multiplied this by 3 to account for maximum deviation from this RMS value. I've seen this method referred to as "Miles' Method".
From here I've used what seems sensible to me to relate this 'vibrational acceleration' to the stresses which result, I was wondering if someone could give me some input on if this is the correct approach as I basically made up this method as I went along but I think it's based on reasonably sound logic. I know the mass of the panel and the acceleration, multiplying these gives the force applied to the panels,this force should act uniformly over the panel rather than as a point load through its centre of gravity (because the entire body is vibrating) so by dividing this force by the area of the panel I can determine an equivalent pressure which would result in the same deformation/acceleration when applied over the panel's surface. Using this pressure value I used a separate ESDU source which allows for the stress in a rectangular panel due to a uniform pressure being applied to be calculated and have taken this stress value to size the thickness of the casing panels. As for the stresses in the bolts, if the bolts pass through the panels into the other sides of the casing i figure all they have to do is react the maximum load which resulted from the vibrational acceleration as this will act perpendicularly to the panel's surface so it's just F/(number of bolts) for the force which each bolt must react and then determine the stress from there and size the bolts to not fail under this stress.
For the shock loading I've done something similar: I used the maximum shock acceleration (given in loading data) multiplied by a dynamic magnification factor (I was told to use a value of Q = 2, not sure if this is correct of not for shock loading?) multiplied by the panel mass to determine the maximum force applied to the panel and then divided this force by the panel's area to find an equivalent pressure and calculated the stress due to this pressure then used this to determine the thickness required to withstand the loading. The final thickness of the panels will be the larger of the thicknesses needed to survive the shock loads and to survive the fatigue loading due to vibration.
Like I said I think this method is based on some decent engineering/physics logic and I realise that there are some simplifications made but without resorting to a finite element model is this a reasonable approach for designing the casing? Any idea how any simplifications that I've made may impact the accuracy of the results? Should this be reasonably close to the stress results which would be observed during testing or miles off? I realise that the plates won't act as simply supported so this is one such simplification. An FE model will be built later of the casing but I'd like to get a feel for the figures first and to make comparisons with the FE results later.
Any input will be much appreciated, looking forward to seeing what people think of this approach...whether they agree with it or think it's complete nonsense really!
Cheers,
Simon
