Free Engineering Tool
Spring Selection by Target Frequency
Calculate the required spring stiffness for a given mass and target natural frequency. Design vibration isolation systems by determining the spring rate needed.
Results
Required Spring Stiffness
Given a mass and a desired natural frequency, the required spring stiffness is derived from the natural frequency equation solved for k:
- m — mass of the supported machine (kg)
- f — target natural frequency (Hz)
- k — required total spring stiffness (N/m); divide by 1000 for N/mm
RPM to Hz Conversion
Static Deflection & Per-Spring Stiffness
Where g = 9.81 m/s² and k is in N/mm for the deflection result in mm.
Practical Example
Given: Machine mass = 300 kg, Target frequency = 4 Hz, 4 springs
ω = 2π × 4 = 25.13 rad/s
k = 300 × (25.13)² = 300 × 631.7 = 189,510 N/m = 189.5 N/mm
δ_static = 300 × 9.81 / 189,510 × 1000 = 15.5 mm
k per spring = 189.5 / 4 = 47.4 N/mm
Equivalent RPM = 4 × 60 = 240 RPM
ℹ️ Design rule: For effective vibration isolation, the natural frequency should be at most 1/3 of the lowest operating frequency. This ensures at least 87.5% isolation.
To select springs for vibration isolation, first determine the mass of the machine and the desired natural frequency of the isolation system. The natural frequency should be well below the operating frequency — typically less than 1/3 of the lowest excitation frequency.
Use the formula k = m × (2πf)² to calculate the required total spring stiffness, then divide by the number of springs to get the stiffness per spring. Verify that the static deflection is acceptable and that the springs can support the load.
For effective vibration isolation, the natural frequency should be at most 1/3 of the lowest operating frequency. For example, if a machine runs at 1500 RPM (25 Hz), the isolation system should have a natural frequency below about 8 Hz.
Lower natural frequencies provide better isolation but require softer springs and larger static deflections. Typical isolation systems target 2–8 Hz depending on the application.
The transmissibility of a vibration isolation system depends on the ratio of operating frequency to natural frequency. Isolation only begins when this ratio exceeds √2 ≈ 1.41.
At a ratio of 3 (natural frequency = 1/3 of operating), transmissibility drops to about 12.5%, meaning 87.5% of vibration is isolated. Below √2, the system actually amplifies vibrations, with the worst case at resonance (ratio = 1).
The number of springs depends on the machine size, weight distribution, and mounting configuration:
- 4 springs — most common, one at each corner for rectangular machines
- 3 springs — triangular layouts
- 6+ springs — large machines requiring distributed support
The total required stiffness is divided equally among all springs. Ensure all springs have equal stiffness to prevent tilting.
Static deflection is the amount a spring compresses under the weight of the supported mass due to gravity (δ = mg/k). It matters because:
- It determines how much the machine sinks on the springs
- It is directly related to natural frequency — larger deflection = lower frequency = better isolation
- The spring must have enough travel for static deflection plus dynamic motion
- Excessive deflection can cause stability issues
Typical isolation springs have 5–25 mm of static deflection.
The procedures described on this page were developed and field-tested by the Vibromera team using the Balanset-1A, a portable dual-channel balancer and vibration analyzer for on-site rotor balancing.
Professional portable balancers, vibration analyzers, and condition monitoring systems used in 50+ countries. Design optimal isolation systems and verify performance on-site.
Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
