Random-Vibration Qualification of an Avionics Bracket: Modal Shift and a Bend-Radius Crack
The avionics unit of a remote-sensing satellite bus is carried on a 6061-T6 sheet bracket, 2 mm thick, with two 90 degree flanges bolted through four M5 inserts to a honeycomb deck. The unit mass is 0.85 kg and the bracket 0.22 kg. The qualification random specification is 14.1 g rms overall from 20 to 2000 Hz, 2 minutes per axis. The finite-element model, with the unit as a rigid mass on a rigid base, predicts the bracket first bending mode at 128 Hz. The pre-test low-level sine sweep measures the first peak at 97 Hz and a second peak at 310 Hz that the model does not predict (the deck panel mode is at 305 Hz). During qualification the base control accelerometer stays within plus or minus 1.5 dB, and the bracket-foot accelerometer records 26.5 g rms. After the run the bracket has a 12 mm crack through its full 2 mm thickness at a flange bend radius, and the four M5 bolts have lost preload.
1. Diagnose the 97 Hz versus 128 Hz gap. Is it a mass error, a stiffness error, or a boundary condition? Quantify before you choose.
Read the worked answer
Quantify each hypothesis
Frequency scales as f proportional to sqrt(k/m), so f_measured/f_predicted = 97/128 = 0.758.
- Pure stiffness deficit: k must be 0.758^2 = 0.574 of the model, i.e. the real bracket is 43% less stiff.
- Pure mass error: m would have to be 1/0.574 = 1.74 times the model, i.e. 1.07 kg becomes 1.86 kg. Only 0.85 + 0.22 = 1.07 kg is actually there, and both masses are weighed. Mass alone is excluded.
So the discrepancy is stiffness, and the question is which stiffness. The model's assumptions are the suspects: a rigid base and a rigid bolted flange. A bracket bolted through four M5 inserts into aluminium honeycomb is not a rigid base - insert compliance and local face-sheet dishing add series compliance at exactly the flange that the model treats as fixed. The second measured peak at 310 Hz against a predicted deck mode of 305 Hz is a strong corroboration: the bracket and the deck panel are coupled, so a rigid-base model is not the right idealisation for this installation.
What to do before believing either number: a free-free or rigid-block modal survey of the bracket alone with the unit mounted, roving hammer, to establish the bracket's own mode; then repeat bolted to the actual deck. If the bracket alone comes in near 128 Hz and only drops to 97 Hz on the deck, the compliance is in the joint and the deck, and the fix is a joint-stiffness and deck-coupling model, not a thicker bracket.
2. The control channel stayed within tolerance, yet the article cracked and the bolts lost preload. Which measurement governs acceptance, and how do you decide whether the design or the test set-up is at fault?
Read the worked answer
The control accelerometer governs the input, not the acceptance. Its job is to prove the specified environment was applied - within plus or minus 1.5 dB here, so the input was legitimate. Acceptance is defined by the article's condition afterwards: no cracks, no loss of bolt preload, no shift in modal response. Both acceptance criteria failed. The run is a fail, regardless of the control trace.
The 26.5 g rms at the bracket foot against 14.1 g rms at the base is a 5.5 times amplification, and that number is diagnostic rather than alarming: a lightly damped mode at 97 Hz sitting inside a 20–2000 Hz broadband input will do exactly that. The article saw a much harsher environment than a rigid-base model with a 128 Hz mode predicted, because the mode is lower and the damping is low (sheet-metal bolted joints typically give 1–3% critical on the fundamental, and the response scales as roughly 1/(2 x zeta)).
Separating design from set-up: first check whether the fixture itself produced an input above spec at the bracket mounting points (it did not, per the control channel, but verify with the foot accelerometer's low-frequency content and a fixture survey). Then check bolt preload as specified versus achieved - a preload lost during the run can be a symptom of joint slip and micro-impact, which is a design and installation issue, not a test issue. Finally look at the crack location: a crack at a flange bend radius is a stress-concentration failure at a Kt of roughly 2, which no amount of mode tuning will remove. Judgment: the design is at fault, and the low measured mode made it worse than predicted. Fix both, not one.
3. The team proposes adding a 0.05 kg doubler at the bend to raise the natural frequency. Evaluate that proposal with numbers, and state what you would change instead.
Read the worked answer
Evaluate the doubler
Mass goes from 1.07 kg to 1.12 kg, a factor of 1.047. Suppose the doubler is generous and raises the local bend stiffness by 50% (k factor 1.5). Then f_new/f_old = sqrt(1.5/1.047) = 1.20, i.e. 97 x 1.20 = 116 Hz. If it only raises stiffness by 30%, f = sqrt(1.30/1.047) = 1.115, i.e. 108 Hz.
Neither is a fix. The mode stays inside the 20–2000 Hz band, so the input is unchanged; the response and the notch stress at the bend are essentially unchanged; and adding mass onto the very flange that is already slipping makes the bolt preload problem worse. The premise is also wrong: the measured 97 Hz is dominated by flange and deck compliance, not by the bend, so local stiffening at the bend buys very little of the 43% stiffness deficit identified earlier.
What to change instead
- Treat the crack as a fatigue problem at a stress raiser: increase the bend radius, remove the undercut, and orient the grain line along the bend.
- Break the load path, not the mode: replace the continuous flange with three short tabs so the bending moment into the deck is reduced, or add a diagonal brace from the unit to the deck to bypass the flange in bending.
- Fix the joint: specify and verify bolt preload with plain washers, use a larger insert footprint, and control the bolt hole clearance; a slipping joint is both a stiffness and a fretting-fatigue source.
- Only after that, re-run the modal survey and check the separation between the bracket mode and the deck mode at 305–310 Hz; then re-qualify. A design change of this size requires a re-qualification, not a delta test, because the failure mode was a crack.