A CNC machine that vibrated the floor. The machine weighed 2 tons. It was bolted to a concrete floor. At high spindle speeds (8000 RPM), the floor rattled. The neighboring office felt the vibration. The customer thought the machine was defective. It wasn’t — the machine’s natural frequency matched the spindle speed. This is about vibration isolation.
The natural frequency
Every mass-spring system has a natural frequency. For a machine on isolation pads:
f_n = (1/2π) · √(k/m)
Where k is the pad stiffness (N/m) and m is the mass (kg). For a 2 ton (2000 kg) machine on hard rubber pads (k = 5,000,000 N/m total): f_n = (1/2π) × √(5,000,000/2000) = 0.159 × √2500 = 0.159 × 50 = 8 Hz. The spindle rotates at 8000 RPM = 133 Hz. That’s way above 8 Hz. But the cutting forces excite at the tooth pass frequency: 4 teeth × 133 Hz = 533 Hz. That’s also above 8 Hz. So why does the floor vibrate?
Because hard rubber pads are too stiff. The isolation efficiency at 133 Hz with f_n = 8 Hz: transmission = (f/f_n)² / ((f/f_n)² – 1) = (16.6)² / (275 – 1) = 275/274 = 0.996. That’s 99.6% transmission. The pads don’t isolate anything. They’re so stiff that the machine and floor vibrate together.
What I changed
1. Switched to coil spring isolators. The spring stiffness is k = 100,000 N/m (much softer). f_n = (1/2π) × √(100,000/2000) = 0.159 × √50 = 0.159 × 7.07 = 1.13 Hz. At 133 Hz: transmission = (133/1.13)² / ((133/1.13)² – 1) = 13,800 / 13,799 = 0.9999. Wait — that’s even worse? No. The formula for isolation efficiency is: T = 1 / (1 – (f/f_n)²). At f/f_n = 118: T = 1 / (1 – 13,924) = -0.00007. The negative sign means isolation (phase shift). The amplitude is 0.007%. That’s 99.99% isolation. The floor doesn’t feel it.
2. Tuned the natural frequency away from excitation. The rule: f_n should be 1/3 of the lowest excitation frequency. For a 50 Hz (3000 RPM) spindle, f_n should be under 16 Hz. For 8000 RPM (133 Hz), f_n under 44 Hz is fine. The hard rubber pads had f_n = 8 Hz — that’s actually in the isolation range. But the rubber pads are so stiff in shear that they transmit vibration through the mounting bolts. I unbolted the machine from the floor and sat it on free-standing spring isolators. The floor vibration dropped by 90%.
3. Checked for resonance. The machine’s internal natural frequency (frame on its mounts) was 25 Hz. The spindle at 1500 RPM (25 Hz) excited the frame resonance. I changed the spindle speed to 1600 RPM (27 Hz) or 1400 RPM (23 Hz) to avoid resonance. The vibration at 8000 RPM was fine — the issue was at low RPM during a facing operation.
Isolation pad selection
| Isolator type | Natural frequency | Isolates | Use for |
|---|---|---|---|
| Hard rubber (bolted down) | 10-30 Hz | Nothing (rigid mount) | Stable machines, no isolation needed |
| Flexible rubber (free-standing) | 5-10 Hz | Over 30 Hz | Light machinery, punch presses |
| Coil spring | 2-5 Hz | Over 10 Hz | Heavy machines, CNC centers |
| Air spring | 1-2 Hz | Over 5 Hz | Precision CMM, measurement |
The isolator I choose: coil spring for CNC machines over 1 ton. The vibrating floor wasn’t the machine — it was hard rubber pads bolted rigidly to the floor. Free-standing springs with f_n under 5 Hz isolate everything above 15 Hz. Don’t bolt the machine to the isolators — let it float.
