Workshop 1: 🛠️ Vibration Isolation & Machine Mounting¶

Industrial & Applied Mechanics Workshop 1 of 6

Vibration Isolation & Machine Mounting

Try it live

Explore this on the interactive simulator with real-time sliders and graphs: 🔬 Launch in Simulator

Workshop Brief¶

Design an isolator mounting for a rotating machine (e.g. a compressor or motor) so that as little of its operating vibration as possible is transmitted into the supporting floor or structure. Too soft a mount lets the machine sway excessively at start-up/shutdown; too stiff a mount barely isolates anything at all at the running speed.

Specifications: Target transmissibility ≤ 0.15 at operating speed · Operating speed 1500 rpm · Machine mass 45 kg

Process Theory¶

A vibrating machine bolted rigidly to a floor transmits essentially all of its shaking force directly into the structure; inserting a resilient mount (a spring, rubber pad, or spring-damper combination) between the machine and the floor converts this into a classic forced-oscillation problem, where the ratio of the force transmitted to the floor to the force generated by the machine — the transmissibility — depends on the ratio of the machine's operating (driving) frequency to the mount's own natural frequency, and on the damping ratio of the mount.

Counter-intuitively, effective vibration isolation requires the mount to be soft, not stiff: transmissibility falls below 1 only once the operating frequency exceeds about 1.4 times the mount's natural frequency, and keeps falling further as the mount is made softer (lower natural frequency) relative to the operating speed. Some damping is still desirable, however, to limit the large transient swing the machine makes as it passes through the mount's own resonance during start-up and shutdown, even though too much damping degrades isolation at the running speed.

The designer's task is therefore to choose a mount stiffness low enough to place the natural frequency well below the operating speed (for good high-frequency isolation) while choosing just enough damping to control the resonance passage, without so much damping that it starts to reintroduce transmitted vibration at the operating speed itself.

Labelled process layout — original schematic prepared for this guide (not a photograph).

Process Parameters¶

Parameter	Range	Unit
Mount stiffness k	500 – 8000	N/m
Damping ratio ζ	0.02 – 0.60	—
Machine mass	20 – 80	kg

Procedure¶

Start with the default mount stiffness and damping ratio and note the transmissibility and verdict shown by the simulator at the given operating speed.
Vary the mount stiffness k alone (holding damping and mass fixed) and record the transmissibility at each setting.
Repeat, varying the damping ratio ζ alone.
From the two sweeps, identify the combination of k and ζ that minimizes transmissibility while keeping the start-up resonance passage acceptably controlled (target: transmissibility ≤ 0.15 for certification).
Record the final certified mount design once the target is reached.

Observation Table¶

Table: Effect of mount stiffness and damping on transmitted vibration

Trial	Stiffness k (N/m)	Damping ratio ζ	Frequency ratio r = ω/ωn	Transmissibility	Verdict
1
2
3
4
5
6
7
8

Graph¶

Plot Transmissibility (y-axis) against Frequency ratio, r = ω/ωn (x-axis).

Expected trend: high near r = 1 (resonance), falling below 1 only once r exceeds about 1.4, and decreasing further as r increases.

📈 Graph paper / plot area — attach printed or digital graph here

Calculation¶

Tabulate transmissibility against each swept parameter and identify the optimum region for each.
State the final mount stiffness and damping combination used to reach the target transmissibility.

Result¶

Table: Optimized isolator mount design

Stiffness k (N/m)	Damping ratio ζ	Frequency ratio r	Final transmissibility	Certified? (Y/N)
1

Precautions¶

Reduce stiffness gradually rather than jumping to extremely soft mounts, which can cause excessive static sag and instability.
Note that too little damping causes a large resonance swing during start-up/shutdown even if it helps the running-speed transmissibility.