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Spring Critical Speed Calculator

Calculate surge frequency and critical speeds for helical springs

Calculation Parameters

Based on ISO 13906 and spring dynamics theory

Metric System

Imperial System

Spring Type

Wire Diameter

Mean Coil Diameter

Number of Active Coils

Spring Material

End Type Configuration

Operating Speed (if rotating)

RPM

Mounting Condition

Critical Speed Analysis Results

First Natural Frequency (Surge):
—

Critical Speed (RPM):
—

Wave Velocity in Spring:
—

Spring Index (C = D/d):
—

Safety Margin:
—

Surge Frequency Assessment:

Safe: Operating < 0.2 × Critical Speed

Caution: Operating 0.2-0.5 × Critical Speed

Warning: Operating 0.5-0.8 × Critical Speed

Danger: Operating > 0.8 × Critical Speed – Redesign required

How the Calculator Works

Spring Surge Phenomenon

Spring surge occurs when the excitation frequency matches the natural frequency of the spring wire, causing resonant vibrations along the spring length.

Natural Frequency Calculation

For helical springs, the first natural frequency is:

fs = (1/2n) × √(G/ρ)

where:

fs — surge frequency (Hz)
n — number of active coils
G — shear modulus (Pa)
ρ — material density (kg/m³)

Critical Speed

The critical rotational speed where surge may occur:

Nc = 60 × fs / k

where k is the harmonic number (typically 1 for fundamental)

Wave Velocity

The velocity of stress waves in the spring material:

c = √(G/ρ)

Spring Index

The spring index affects surge behavior:

C < 4: Difficult to manufacture, high stress
C = 4-12: Normal range for most springs
C > 12: Prone to tangling and buckling

Material Properties

Material	Shear Modulus (GPa)	Density (kg/m³)
Music Wire	81.7	7850
Stainless 302	69.0	7900
Chrome Silicon	77.2	7850
Phosphor Bronze	41.4	8800

Prevention Methods

Design spring natural frequency > 13× operating frequency
Use variable pitch springs to break up resonance
Add damping (nested springs, coatings)
Change spring dimensions or material
Use surge dampeners or spring guides

Effects of Surging

Premature fatigue failure
Coil clash and impact damage
Loss of load capacity
Excessive noise and vibration
Unpredictable spring behavior

📘 Critical Speed Calculator (Spring Surge)

Calculates surge frequency and critical speed for helical springs. Surge occurs when spring coils vibrate at resonance, causing stress and failure.
Formula: fs = c/(2L) where c = wave velocity, L = wire length.

💼 Applications

Engine Valve Spring: Operating 6000 RPM = 100 Hz. Spring surge frequency: 250 Hz. Safety ratio: 100/250 = 0.4 < 0.5 ✓ Safe. Higher spring index or fewer coils increases surge frequency.
Vibration Isolator: Equipment 1480 RPM. Springs must not surge. Calculated: 3500 RPM critical. Ratio: 1480/3500 = 0.42 ✓
Compressor Pressure Relief: Spring in valve, rapid cycling 60 Hz. Surge: 180 Hz. Safe but check for harmonics at 2× and 3× operating frequency.

Surge Prevention:

Design Rules: Operating frequency should be < 0.5 × surge frequency. For critical applications: < 0.3 × surge frequency.

Solutions if too close: Increase wire diameter, decrease mean diameter, reduce active coils, use damping sleeves, nested springs.

Spring Critical Speed (Surging) Calculator

Published by admin on October 20, 2025 October 20, 2025