Torsion Spring
Helical torsion spring: M = k×θ. Spring rate k from wire diameter, mean diameter, active coils. Bending stress in wire. Used in clothespins, hinges.
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M = kθ; linear torque-deflection. Rate k ∝ d⁴/D; wire size dominates. Stress limits fatigue life. Leg geometry affects moment arm.
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Why: Torsion springs store rotational energy. Used in clips, hinges, ratchets. Rate and stress determine life and load.
How: M = k×θ. Rate depends on E, d, D, n. Bending stress limits load. SMI and ASME provide design standards.
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🔩 Steel Torsion Spring
d=1mm, D=12mm, 5 turns, music wire
🔄 Torque Calculation
k=0.05 N·m/rad, θ=45°
💪 Force at Arm
5N force at 20mm arm
🛡️ Stainless Torsion
Corrosion resistant design
⚡ Heavy Duty Spring
Large torsion spring
Spring Geometry
Material Properties
❓ Frequently Asked Questions
What is a torsion spring and how does it work?
A torsion spring is a mechanical device that stores rotational energy when twisted. Unlike compression or extension springs that work along their axis, torsion springs deliver torque tangent to the coil axis. When one or both legs are rotated around the coil axis, the spring exerts a torque in the opposite direction proportional to the angular deflection. The spring rate (k) defines this relationship: M = k × θ.
What is spring index and why is it important?
Spring index (C = D/d) is the ratio of mean coil diameter to wire diameter. It's a critical manufacturability measure. Keep spring index between 4-12 for optimal results. Too low (C < 4) makes coiling difficult and increases manufacturing costs. Too high (C > 12) can lead to instability and tangling. Most commercial springs have C between 6-10.
What is the stress correction factor and why is it needed?
The stress correction factor (Ki for inner radius, Ko for outer radius) accounts for the curvature effect in helical springs. Bending stress is higher on the inner radius of the coil due to curvature. Ki = (4C² - C - 1) / (4C(C-1)) corrects for this effect. Always use the inner radius correction factor (Ki) for conservative stress calculations, as it's always larger than Ko.
What safety factor should I use for torsion spring design?
A safety factor of 1.5-2.0 is typically recommended for torsion springs. Safety factor below 1.0 indicates failure will occur. Between 1.0-1.5 is marginal and should be avoided for critical applications. For high-cycle applications or dynamic loading, use safety factors of 2.0 or higher. The calculator uses 75% of tensile strength as allowable stress, which is conservative for most applications.
Why does the inner diameter decrease under load?
When a torsion spring is deflected, the coils wind tighter, causing the mean diameter and inner diameter to decrease. This is calculated as: D_new = (Nb × D) / (Nb + θ_coil). This diameter reduction is important for clearance considerations - ensure the pivot or shaft has adequate clearance to prevent binding. Typically, diameter reduction of more than 10% requires careful design review.
How do leg lengths affect spring performance?
Leg lengths contribute to active coils through the formula: Ne = (L1 + L2) / (3πD). Longer legs increase the effective number of active coils, which decreases spring rate (makes the spring softer) and increases angular deflection for the same torque. Leg design also affects how the spring attaches to the application and influences stress concentrations at the leg-to-body transition.
What materials are best for torsion springs?
Music wire (ASTM A228) offers the highest tensile strength (2585 MPa) and is excellent for high-stress applications. Chrome vanadium and chrome silicon provide good fatigue resistance. Stainless steel (302/304/316) is used for corrosion resistance. Phosphor bronze and beryllium copper offer good electrical conductivity. Choose material based on application requirements: strength, fatigue life, corrosion resistance, temperature, and cost.
How accurate are these calculations?
Calculations provide theoretical estimates based on standard formulas from SMI and ASME standards. Actual performance may vary due to manufacturing tolerances, material property variations, surface finish, heat treatment, and end conditions. For critical applications, always verify with prototype testing and consult with spring manufacturers. The formulas assume uniform material properties and ideal geometry, which may not match actual manufactured springs.
📚 Official Data Sources
SMI Spring Standards
Spring Manufacturers Institute standards and specifications
Last Updated: 2026-01-15
ASME Spring Design Standards
American Society of Mechanical Engineers spring design standards
Last Updated: 2026-01-20
MIT OCW Mechanical Design
MIT OpenCourseWare mechanical design and spring theory
Last Updated: 2025-12-01
⚠️ Disclaimer: This calculator provides theoretical torsion spring design estimates based on standard formulas from SMI and ASME standards. Actual spring performance may vary due to manufacturing tolerances, material property variations, surface finish, heat treatment, end conditions, and environmental factors. Stress calculations assume ideal geometry and uniform material properties. For critical applications, always verify designs with prototype testing and consult with qualified spring manufacturers. Safety factors should be increased for high-cycle applications, dynamic loading, or harsh environments. This calculator is for educational and preliminary design purposes only and is not a substitute for professional engineering analysis.
For educational and informational purposes only. Verify with a qualified professional.
🔬 Physics Facts
M = kθ; torque proportional to angle.
— Springs
Rate k from wire d, mean D, coils n.
— SMI
Bending stress σ = 32M/(πd³).
— Design
Helical torsion: wire bends, not twists.
— Mechanics
📋 Key Takeaways
- • Torsion springs store rotational energy; torque M = k × θ (spring rate × angular deflection)
- • Spring rate k = (E × d⁴) / (64 × D × Na) depends on wire diameter, mean diameter, and active coils
- • Spring index C = D/d should be 4–12 for manufacturability
- • Stress correction factor Ki accounts for curvature; use inner radius for conservative design
- • Inner diameter decreases under load—ensure adequate pivot clearance
What is a Torsion Spring?
A torsion spring is a mechanical device that stores rotational energy when twisted. Unlike compression or extension springs that work along their axis, torsion springs deliver torque tangent to the coil axis. They're used in applications requiring rotational force, from clothespins and mouse traps to garage doors and automotive components.
Key Components
- • Wire diameter (d)
- • Mean coil diameter (D)
- • Body turns (Nb)
- • Leg lengths (L1, L2)
- • Angular deflection (θ)
Common Applications
- • Clothespins and clips
- • Garage door mechanisms
- • Mouse traps
- • Hinges and lids
- • Automotive components
How Does a Torsion Spring Work?
A torsion spring works by storing energy when one or both legs are rotated around the coil axis. The spring exerts a torque in the opposite direction proportional to the angular deflection. The spring rate (k) defines this relationship.
Key Relationships
Torque-Deflection
M = k × θ
Torque equals spring rate times angular deflection
Spring Rate
k = Ed⁴ / (64DNa)
Depends on material and geometry
When to Use Torsion Springs?
| Application | Why Torsion Spring? |
|---|---|
| Hinges & Doors | Rotational motion, self-closing |
| Clips & Clamps | Gripping force through rotation |
| Counterbalancing | Lift assistance (garage doors) |
| Return Mechanisms | Returning to rest position |
Essential Torsion Spring Formulas
Spring Rate
k = (E × d⁴) / (64 × D × Na)
E = Young's modulus, Na = active coils
Angular Deflection
θ = (64 × M × D × Na) / (E × d⁴)
Result in radians
Bending Stress
σ = K × (32 × M) / (π × d³)
K = stress correction factor
Stress Correction (Ki)
Ki = (4C² - C - 1) / (4C × (C - 1))
For inner radius (always larger)
Design Considerations
Spring Index (C = D/d)
Keep between 4-12 for manufacturability. Too low = difficult coiling. Too high = instability.
Diameter Reduction
Inner diameter decreases under load. Ensure clearance with pivot/shaft.
Leg Design
Leg lengths affect active coils. Longer legs = more deflection at same torque.
Direction of Wind
Load should wind the spring tighter (close the coils), not open them.
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