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Isolator Transmissibility Explorer

Run the Isolator Transmissibility Explorer MicroSim Fullscreen

About This MicroSim

How much of a fan's unbalance force gets through its isolators depends on how far apart the fan's speed and the isolators' bounce are. This MicroSim uses the undamped single-degree-of-freedom model from Chapter 22:

  • forcing frequency f = N / 60 (Hz), from the fan speed N in RPM;
  • natural frequency fn = 3.13 / √δ (Hz), from the static deflection δ in inches (the rounded form of (1/2π)√(386.1/δ));
  • frequency ratio r = f / fn;
  • transmissibility T = 1 / |r² − 1|, and percent isolation (1 − T) × 100.

The chart plots T on a log scale against r from 0 to 10. The band below r = 1.414 (√2) is shaded and labeled Amplification, the rest Isolation, and the dotted line at r = 1 marks Resonance. The readouts give f, fn, r, T and the percent isolation; when T is greater than 1 they show "amplified ×T" instead of a negative percentage, and within 0.05 of r = 1 they show "at or near resonance" (the plotted T is capped at 10). Values are shown to 3 significant figures; answers are judged against the unrounded model.

Three challenges come first, in a fixed order. You type T before the curve is shown; an answer within ±5% of the model counts as correct. Each challenge allows two attempts.

# Fan speed Deflection Model T What it shows
1 1170 RPM 1.0 in (spring) 0.0264 about 97.4% isolation
2 1170 RPM 0.0625 in (neoprene pad) 0.701 only about 30% isolation
3 600 RPM 0.0625 in (neoprene pad) 2.76 r = 0.80, the pad amplifies the force

Mastery is 3 of 3 on the first attempt. After challenge 3, Explore mode unlocks the fan speed (300 to 3,600 RPM in 30 RPM steps) and the six deflections from FanPedia p. 134: 0.0625 in (neoprene pad), 0.2, 0.3 and 0.5 in (rubber-in-shear), 1.0 and 2.0 in (spring). The fan speeds are illustrative.

How to Use

  1. Read challenge 1. The fan speed and deflection are set for you; the readouts show "?".
  2. Type T as a decimal in Transmissibility T and press Check (or Enter). A correct answer reads, for example, "Correct: T = 0.0264, 97.4% isolation." A wrong first answer shows the challenge's worked numbers and "Try again (1 attempt left)."; after a second wrong answer the answer and worked calculation are shown and the challenge counts as missed.
  3. Once a challenge ends, the curve appears with the model's operating point (square) and your answer (open diamond) side by side, and the readouts fill in. Press Next challenge.
  4. After challenge 3, press Finish for the summary ("First-attempt score: n of 3" and the mastery line). Explore mode then unlocks: move the Fan speed slider and change the Deflection; the point, readouts and region label update at once. Try 420 RPM with 0.2 in (resonance), and any pad setting below about 1,060 RPM (amplification). Explore mode is never scored.
  5. Press Start over at any time to begin again from challenge 1.

Keyboard: Enter checks your answer, then goes to the next challenge. In Explore mode the arrow keys move the speed slider in 30 RPM steps and change the deflection; Tab reaches every control.

Data label: "Illustrative fan speeds · Deflections: FanPedia p. 134 · Undamped model: f = N/60, fn = 3.13/√δ, T = 1/|r² − 1|", shown under the chart.

Iframe Embed Code

You can add this MicroSim to any web page by adding this to your HTML:

<iframe src="https://moroshek.github.io/FanTASTIC-textbook/sims/ch22-isolator-transmissibility-explorer/main.html"
        height="872px"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Learning Objective

The learner will calculate the transmissibility of an undamped isolator from the fan speed and the isolator's static deflection, to within 5% of the model value (Bloom: Apply, verb: calculate).

Audience

Adult professional development: new application engineers, sales staff, representatives and facilities staff.

Duration

10-15 minutes

Prerequisites

  • Forcing frequency and natural frequency
  • Frequency ratio, transmissibility and percent isolation
  • Static deflection
  • Resonance

All are defined in the "Vibration", "Vibration Isolation" and "Isolator Deflection" sections of Chapter 22.

Activities

  1. Calculate (6 min): Work the three challenges with a calculator, committing T before the curve appears.
  2. Explore (5 min): Repeat the chapter's 600 RPM table (pad, rubber-in-shear 0.3 in, springs 1 in and 2 in). Find the speed where the pad leaves the amplification region (about 1,060 RPM) and the resonance at 420 RPM with 0.2 in.
  3. Discuss (3 min): Why does the same pad isolate a 1,770 RPM fan but amplify a 600 RPM fan? What happens to fn when the deflection doubles from 1 in to 2 in?

Common Misconceptions Addressed

  • Any isolator reduces transmitted force: challenge 3 gives T = 2.76, more force than a rigid mount, because r < 1.414.
  • An isolator that works on one fan works on any fan: challenges 2 and 3 use the same pad at two speeds, with opposite results.
  • Doubling the deflection halves the natural frequency: in Explore mode, 1 in gives 3.13 Hz and 2 in gives 2.21 Hz, a factor of √2.

Assessment

  • Running score "Challenges correct: n of 3"; the summary shows "First-attempt score: n of 3" with "Mastery reached (3 of 3 needed)." or "Mastery needs 3 of 3 on the first attempt."
  • Follow-up: a fan runs at 900 RPM on rubber-in-shear mounts deflecting 0.5 in. Calculate T and the percent isolation, then check it in Explore mode.

References

  1. FanPedia: The Fan & Blower Encyclopedia - Twin City Fan. Isolator types and deflections, p. 134; vibration isolation, p. 133.
  2. Chapter 22: Fan Bases and Vibration Isolation - the chapter section this sim belongs to, with the worked examples it reproduces.
  3. Vibration isolation - Wikipedia, background on transmissibility and the frequency ratio.
  4. Plotly JavaScript log axes - the chart's log scale.