Torsion spring design is one of the most misunderstood areas of spring engineering. Unlike compression and extension springs, which carry axial loads, a torsion spring works in rotation: a torque twists its coiled body around its own axis, storing energy that returns a mechanism to its starting position. In short, a torsion spring is a coiled bar working in bending. Getting legs, wind direction and rate right is what separates a spring that lasts a million cycles from one that fails after a few thousand.
How a Torsion Spring Works: Legs, Body and Torque
A torsion spring consists of a coiled body with two legs (also called ends or arms). The body is the working part; the legs transmit the applied torque. When a force is applied to one leg while the other is held, the body winds tighter or unwinds, resisting with a torque proportional to the deflection angle.
Three definitions matter before any calculation:
– Torque (T): the twisting moment applied to the spring, usually in N·mm or N·m.
– Deflection angle (θ): the angular travel in degrees or radians.
– Spring rate (k): the torque required per degree of deflection, in N·mm/deg.
Because torsion springs act in bending — despite the name — the wire tolerates higher stresses than a compression spring of the same size. If you are still comparing spring types, our article Compression vs. Extension vs. Torsion Springs helps you match the type to the load case.
Leg Design and Wind Direction: Get These Right First
The legs are where most design mistakes happen. Common leg styles include straight torsion ends, straight offset ends, hinged ends and short hook ends. The leg style is dictated by how the spring mounts — a hinge end grips a pin, an offset end hooks over a stop, a straight leg drops into a slot.
Wind direction is the second decision: a right-hand wound spring coils clockwise, a left-hand wound spring counter-clockwise. The hand determines how the legs orient under load and which way the torque acts. A common error is the wrong hand — it unwinds the spring instead of winding it tighter. On the drawing, state the hand explicitly and show which leg is fixed and which is loaded.
A double torsion spring — two bodies wound in opposite directions joined by a center leg — shares the load and delivers balanced torque without the side thrust of a single body. Double torsion designs suit clothespins, clips and counterbalance mechanisms where space is tight; the garage door spring buying guide shows how torsion springs balance heavy doors in exactly this way.
Torsion Spring Calculation: Rate and Stress Formulas
The standard torsion spring rate formula used in spring design is:
k = E · d⁴ / (3667 · D · n) (N·mm per degree)
where E is the elastic modulus (MPa), d the wire diameter (mm), D the mean coil diameter (mm) and n the number of active coils. The constant 3667 converts the bending formula to N·mm per degree; in radians use k = E·d⁴ / (64·D·n).
The bending stress at the wire surface is:
σ = 32 · T · K / (π · d³)
where K is a curvature correction factor — stress concentrates on the inner diameter of the coil, so applying K (around 1.1–1.3) prevents underestimating the peak stress. Keep the spring index C = D/d between 4 and 16; a lower index stresses the inner fiber heavily, a higher index makes the spring bulky.
A practical design loop: fix the working space (OD, ID, free length) → choose wire diameter and active coils → calculate the rate → check bending stress at the maximum deflection angle → adjust d or n until both fit. Remember the body grows slightly in diameter as it winds up; allow clearance against any surrounding bore.
Materials, Tolerances and Assembly Details
Because torsion springs bend the wire, material choice follows bending fatigue rules. Music wire (ASTM A228) suits small, lightly loaded springs; chrome silicon (ASTM A401) handles higher stresses and dynamic loads; stainless grades such as 302 and 17-7PH add corrosion resistance. Our spring steel materials guide compares these grades for load and environment.
Specify leg angle tolerances realistically: ±2° on precision springs, ±5° as a commercial tolerance. State the free, loaded and maximum positions on the drawing — three positions beat two. For indexing, note the gap between adjacent coils and the coiling direction with an arrow. Our spring engineering notes cover manufacturing limits such as arbor size, mandrel clearance and leg bend radii.
FAQ
What is the formula for torsion spring rate?
Use k = E·d⁴ / (3667·D·n) for deflection in degrees, where E is the elastic modulus, d the wire diameter, D the mean coil diameter and n the active coils; the legs add little to the rate.
What is the maximum deflection for a torsion spring?
There is no universal limit — safe travel depends on stress. Keep bending stress below about 60–70% of tensile strength for static service, far lower for fatigue; avoid winding a single-body spring past 360° without checking stress first.
Should my torsion spring wind up or unwind as it is loaded?
It should wind tighter, never unwind — the applied torque should close the coils. If the mechanism would unwind it, reverse the wind direction or the leg position — unwinding opens the coils and can allow the body to bind or the legs to slip.
How do I choose between a single and a double torsion spring?
A double torsion spring balances the torque and eliminates side thrust — the standard choice for short, compact mechanisms. A single body is simpler and cheaper when space and side load are not concerns.
Still unsure about your torsion spring design? Send us a drawing or sketch with the working space, torque, deflection angle and leg style — our engineers will check the rate, stress and material choice. Contact the Chenji team for a quotation, or email liu@chenjisprings.com / call +86 158 5311 1612. We have manufactured custom torsion springs since 2003 and inspect every batch.