Induced-Draft Fan Frame Resonance After a Motor Upgrade
A cement plant replaced the induced-draft fan serving its kiln baghouse. The new fan runs at 990 rpm and is driven by a 160 kW motor. The fan and motor together add 210 kg to the existing structural steel frame, which now supports 1,150 kg at the fan deck. A bump test before the upgrade gave a first horizontal natural frequency of 21.0 Hz; after the upgrade, the same test gives 18.3 Hz. At first run the fan inboard bearing reads 9.4 mm/s RMS overall, dominated by a peak at 16.5 Hz with a smaller component at 33 Hz; the fan was balanced to Grade 6.3 before installation and alignment was checked with a laser. The contractor proposes to accept the condition because 'it is under 11 mm/s' and the kiln must be back on line within five days. The structural designer estimates that two diagonal braces would raise the frame's lateral stiffness by 70% and add 60 kg of steel, and would consume three days of the shutdown window. Kiln output is worth about $95,000 per day when lost.
1. Assess whether this is resonance, using the frequency data, and judge whether the contractor's acceptance argument is defensible.
Read the worked answer
Frequency ratio. Running speed 990 rpm = 16.5 Hz. Measured first natural frequency 18.3 Hz. Ratio f_n/f_run = 18.3/16.5 = 1.11. That sits inside the band where the dynamic amplification is severe; many structural and rotating-machine criteria demand that a natural frequency be at least 20% away from, or 1.5–2 times, the excitation frequency. Before the upgrade the ratio was 21.0/16.5 = 1.27, already marginal - so this frame was never robust, and the added mass tipped it over.
Consistency check. Adding 210 kg to what was a 940 kg deck should lower the frequency by √(940/1150) = 0.90, predicting 21.0 × 0.90 = 19.0 Hz. Measured 18.3 Hz is close, which raises confidence that the bump test is genuine rather than an artefact.
Amplification estimate. For a ratio r = 1.11 and light damping (ζ ≈ 0.02 for a welded frame), magnification ≈ 1/√[(1 − r²)² + (2ζr)²] = 1/√[(1 − 1.232)² + (0.044)²] ≈ 4.2. A fan balanced to Grade 6.3 that would normally produce about 2 mm/s is therefore reading 9.4 mm/s - the vibration is the residual unbalance multiplied by the frame, not a fan fault. The 33 Hz component is simply 2× running speed, amplified by the same mechanism.
The acceptance argument fails for three reasons: a single overall velocity number without a frequency or phase analysis cannot distinguish a balanced machine on a resonant frame from a defective machine; the threshold quoted has no basis in the machine's own specification or in a recognised zone standard for this class of machine; and a resonant support produces fatigue at the brace and anchor welds, so the risk is not only vibration nuisance but a structural crack that develops over months. Confirm with a run-up or coast-down (Bode) plot - an approximately 90° phase shift and a peak at 16.5 Hz as the machine passes through its natural frequency is conclusive.
2. Evaluate the brace proposal quantitatively, decide whether to spend the three days, and state the natural-frequency criterion you would apply.
Read the worked answer
Predicted effect of the braces. Natural frequency scales as √(k/m):
f_new = 18.3 × √(1.70 × 1150/1210) = 18.3 × √1.616 = 18.3 × 1.271 = 23.3 Hz
Ratio to running speed = 23.3/16.5 = 1.41.
Judgement on the criterion. A ±20% separation criterion would be satisfied (the forbidden band is roughly 13.2–19.8 Hz). A 1.5× separation criterion would not - that needs 24.75 Hz. To reach 24.75 Hz, stiffness must rise by (24.75/18.3)² × (1210/1150) = 1.83 × 1.05 = 1.92, i.e. about +92%, not +70%. So the proposal gets most of the way but leaves the frame 6% below a 1.5× target, which in practice means it should be modelled before fabrication rather than assumed.
Decision. Spend the three days. The cost is 3 × $95,000 ≈ $285,000 of lost output. Against that, the alternative is restarting a resonant frame carrying a 160 kW fan, with a credible path to fatigue cracking at brace or anchor welds, an unplanned second outage, and a much larger production loss. The three days are also the only opportunity to make the change without a second shutdown.
However, do not accept the brace as a finished answer. Instruct the designer to model the braced frame, including the torsional mode, and to size the bracing to reach at least 1.5× running speed if the geometry allows, or to confirm in writing that 1.41 is acceptable with damping and a monitoring regime. Options that do not work: adding mass lowers the frequency and makes matters worse; changing fan speed is no help because 900 rpm gives a ratio of only 1.22 and any speed near 1,100 rpm lands on the natural frequency.
3. Set out the checks and acceptance criteria you would require before the kiln is restarted with the modified frame.
Read the worked answer
Before restart - verification of the change:
- As-built confirmation that the braces, gussets and base plates match the design, with weld procedures and inspection (visual plus MPI or UT on complete-joint-penetration welds) recorded.
- Anchor bolts and grout checked; the added load path must reach the foundation, not just stiffen the deck locally.
- A bump test on the modified frame, in both horizontal directions plus torsion, witnessing a first natural frequency at least 20% clear of 16.5 Hz and of blade-pass frequency; compare against the model prediction of 23.3 Hz.
- Fan alignment re-checked after the structural work and the fan re-balanced if the residual unbalance is above the original Grade 6.3 balance quality; a balanced rotor on a stiffened frame should fall well below 4.5 mm/s.
During and after run-up:
- A run-up or coast-down sweep to show no resonance crossing within the operating range, and a phase-stable 1× vector at steady state.
- Acceptance: overall velocity within the zone limit applicable to this machine class and mounting, with 1× amplitude at the inboard bearing no more than about half the pre-modification value. Set an alarm at a level roughly 1.5 times the settled value and a trip or mandatory shutdown at the applicable zone C/D boundary, rather than relying on a single fixed number.
- Weekly trended readings for the first month, then monthly, watching for a rising 1× (unbalance or cracking) and for any change in the natural frequency indicated by a shift in the spectrum.
Documentation. Record the pre-modification baseline, the modification, the post-modification bump test and the acceptance readings in the asset register so that the next motor change does not repeat the original error of adding mass without re-checking the frequency.