CORE PRINCIPLES
What to establish first
- Wire diameter has a fourth-power effect on a helical spring's rate.
- Mean coil diameter and active-coil count set flexibility.
- Spring index is a geometry screen, not a fatigue approval.
Springs
Helical, leaf and torsion spring geometry, stress and rate.
MODULE OVERVIEW
Springs in practical engineering work.
A spring stores energy and provides a controlled force-deflection response. Rate, stress, solid height, buckling, end condition and fatigue must be considered together.
DESIGN CONCEPTS
Terms worth checking
- Spring rate
- Active coils
- Spring index
Common applications: Valve and return springs · Vibration isolation · Latches and force-controlled mechanisms
KEY RELATIONSHIP
Close-coiled compression-spring rate
k = Gd⁴/(8D³N)
- G — shear modulus, N/mm²
- d — wire diameter, mm
- D — mean coil diameter, mm
- N — active coils
The equation describes elastic, close-coiled round-wire behaviour and does not calculate stress.
WORKED EXAMPLE
Known values → substitution → interpretation
- Known values
- G = 79 GPa; d = 5 mm; D = 35 mm; N = 8
- Method
- Convert G to 79,000 N/mm² and substitute
- Interpretation
- The preliminary rate is about 18.0 N/mm; verify stress, travel and solid height before manufacture.
KEY DESIGN CHECKS
Confirm the conditions behind the number
- Define the governing load case, duty cycle and required design life before using a simplified relation.
- Use compatible units and material data for the actual condition, temperature and manufacturing state.
- Compare the result with strength, stiffness, fatigue, safety, serviceability and applicable-code requirements.
COMMON ENGINEERING MISTAKES
Keep the model within its scope
- Applying close-coiled compression-spring rate outside the assumptions shown on this page.
- Using a nominal condition while a peak, alternating, transient or environmental case governs the design.
- Treating a calculated value as a final component selection without checking interfaces, tolerances and the current governing standard.
AVAILABLE CALCULATORS
Select a calculator
RELATED RESOURCE
Open Spring Rate Calculator
Change wire and coil geometry to see the live spring response.
Open related resource →REFERENCES & LIMITATIONS
Use this content as a transparent starting point
ReferenceA. M. Wahl, Mechanical Springs; supplier spring-design data for material and end-condition limits.ScopeRelationships are presented for the assumptions stated on this page and linked tool.Design reviewCheck material condition, loads, environment and the applicable current code.SafetyResults are educational/preliminary and do not certify safety or compliance.
RELATED ENGINEERING