Torsion Spring Calculator
Calculate torsional spring parameters, torque, angular deflection, and stress
Torsion Spring Calculator
Spring Parameters
Steel: 200 GPa, Stainless: 193 GPa
Applied Load
Distance from spring center to force application point
Basic Results
Angular Deflection Formula: θ = (64 × M × D × Na) / (E × d⁴)
Spring Rate: k = M / θ = 0.0000 N⋅m/rad
Spring Rate per Turn: 0.0000 N⋅m/turn
Example Calculation
Steel Torsion Spring Example
Wire diameter (d): 1.0 mm
Mean coil diameter (D): 12.0 mm
Number of active turns (Na): 5
Young's modulus (E): 200 GPa
Applied torque (M): 0.05 N⋅m
Calculation
θ = (64 × M × D × Na) / (E × d⁴)
θ = (64 × 0.05 × 0.012 × 5) / (200×10⁹ × (0.001)⁴)
θ = 0.192 / (200×10⁹ × 1×10⁻¹²)
θ = 0.192 / 0.2 = 0.96 rad = 55°
Spring rate: k = 0.05 / 0.96 = 0.052 N⋅m/rad
Torsion Spring Types
Helical Torsion Spring
Wire coiled in cylindrical shape with straight ends for applying torque
Torsion Bar
Straight bar that twists about its own axis under applied torque
Key Formulas
Angular Deflection
θ = (64 × M × D × Na) / (E × d⁴)
Spring Rate
k = M / θ
Torque
M = F × r
Bending Stress
σ = K × (32 × M) / (π × d³)
Material Properties
Design Guidelines
Spring index (C = D/d) should be 5-15 for good performance
Legs should be long enough to prevent overstress
Consider diameter reduction under load
Inner stress correction factor (Ki) is always higher
Hooke's law doesn't apply to torsion springs
Understanding Torsion Springs
What is a Torsion Spring?
A torsion spring is a mechanical device that stores and releases rotational energy. Unlike compression or tension springs that work linearly, torsion springs operate by twisting around their axis to provide torque.
Key Components
- •Mean Diameter (D): Average diameter of the coil
- •Wire Diameter (d): Thickness of the spring wire
- •Active Turns (Na): Coils that contribute to deflection
- •Legs: Straight ends where torque is applied
Diameter Relationships
Outer Diameter: Do = Di + 2d
Mean Diameter: D = Di + d
Spring Index: C = D / d
Angular Deflection
The angular deflection of a torsion spring is calculated using the relationship between applied torque, material properties, and spring geometry.
θ = (64 × M × D × Na) / (E × d⁴)
- θ: Angular deflection (radians)
- M: Applied torque (N⋅m)
- D: Mean coil diameter (m)
- Na: Number of active turns
- E: Young's modulus (Pa)
- d: Wire diameter (m)
Stress Analysis
Bending stress in a torsion spring varies across the wire cross-section. Stress correction factors account for this variation.
Applications
Household Items
- • Clothespins
- • Mousetraps
- • Garage door hinges
- • Clipboards
Industrial
- • Counterbalance mechanisms
- • Hinge return systems
- • Ratchet mechanisms
- • Rotary actuators
Automotive
- • Suspension systems
- • Throttle return springs
- • Clutch mechanisms
- • Window regulators