Torsion springs

Lee's LTL012A01M lists a 90° free leg position and 0.050 lbf·in at 90° deflection. Those angles use different datums. Assuming linear rate from zero torque gives 0.025 lbf·in at 45° deflection. At the rated torque and 0.188 in radius, perpendicular force is about 0.266 lbf. Check winding direction, loaded clearance and fatigue separately. Lee catalog, pp. 287–288.

Construction and physical action

The legs apply torque while the wire primarily bends. Coil spacing can reduce friction and hysteresis. Lee Spring, Torsion springs, construction and design considerations.

Leg shapes set the contact and restraint. Double-torsion springs combine left- and right-hand bodies. Newcomb Spring, Torsion Springs, single-page design sheet.

Winding direction, loading direction and angle datum

Right- or left-hand winding describes the helix. Loading direction describes how the legs move relative to one another. Newcomb's guidance favors loading that tightens the coil. “Clockwise” alone is incomplete without the viewing direction and the leg held stationary: reversing the view reverses the apparent rotation. This viewpoint distinction is explanatory geometry, not a universal right-hand/clockwise selection rule. Newcomb, Right vs. left hand helical spring wind direction.

Free angle is the angular separation of the unloaded legs. Angular deflection is their relative movement from that free state; an installed or final leg angle is a position. Newcomb also notes that spring index and active-coil count affect free-angle tolerance. An angle label therefore has both a geometric datum and a manufacturing tolerance, not just a number. Newcomb, Torsion spring free angle.

For a simple coplanar example, let the oriented free separation be α0 and define positive θ as motion closing that separation. On that chosen branch, α = α0 − θ. Thus α0 = 90° and θ = 30° give α = 60°. This is a declared geometric convention, not a rule for interpreting every supplier's 0°/360° drawing. Absolute leg position, free position and travel are different quantities. Newcomb, Helical spring deflection.

Torque, angular rate and leg effects

Lee defines angular rate as torque per unit angle. Explanatory linear models are M ≈ kθ from an unloaded datum, or M ≈ M0 + kΔθ with installed preload M0 and incremental travel Δθ. They are not measured hysteresis curves; angle units must match k. Lee, Torsion spring terminology.

One revolution equals 360° or 2π radians. Consequently:

• k per radian = k per degree × 180/π.
• k per revolution = k per degree × 360.
• A value in N·mm/degree cannot be multiplied directly by an angle in radians.

These are unit conversions; they do not change the physical spring. Newcomb's round-wire approximation uses turns, not degrees: M = E d⁴ n / (10.8 N D), where n is deflection in revolutions, N is coil count in that approximation, D mean coil diameter, d wire diameter and E elastic modulus. Substituting degrees for n would produce a factor-of-360 error. Newcomb, design sheet, formula panel.

Leg flexibility also stores energy. Newcomb explicitly includes flexing portions of a straight lever in the active spring material. Thus a coil-only rate estimate need not equal the installed rate measured between remote leg contacts. Changing contact location or leg restraint can change the measured response even when body and wire diameters stay the same. Newcomb, Active coils in a helical spring.

Bending stress and operating clearance

For round wire, Newcomb gives bending stress as σ = KB × 32M/(πd³), where KB corrects for curved-wire stress distribution. With M in N·mm and d in mm, σ is N/mm², or MPa. The inside surface can be more highly stressed than the outside. This relationship is a stress model, not an allowable stress or cycle-life rating. Newcomb, Torsion spring stress, attributed to the Spring Manufacturers Institute.

Sharp leg bends may carry higher stresses than the coiled body. Forming marks, bend geometry and frictional contact can make the ends critical in cyclic operation. A body stress calculation alone therefore cannot establish fatigue life or permissible travel. Newcomb, Torsion spring ends, Cyclic operating stress.

Winding the spring tighter reduces coil diameter and increases body length. An arbor that fits the unloaded bore can therefore bind during travel; an axially confined body can also interfere as it lengthens. Newcomb's design sheet describes support by a shaft or tube with clearance throughout deflection. Initial bore size alone establishes neither the working arbor size nor adequate housing clearance. Newcomb, design sheet.

Bounded example: Lee Spring LTL012A01M

Lee’s 2019 Product Catalog identifies LTL012A01M: left-hand wound music wire, 90° free position. Lee catalog, pp. 287–288.

The finish specification is 0.0002 in zinc plating; wire ≤0.025 in may instead be pre-coated without supplemental zinc at Lee's discretion. This example qualifies for that exception. Torque tolerance is ±10%; rate is derived below. Lee catalog, p. 286 and p. 288 footnotes.

Nominal rate and lever-force arithmetic

Using the catalog torque and deflection with an assumed linear, zero-torque free datum:

• k = 0.050/90 = 0.000556 lbf·in/degree.
• k = 0.0318 lbf·in/radian after the 180/π conversion.
• At 45° deflection, M ≈ 0.025 lbf·in by direct proportion.

This is nominal arithmetic within the illustrated range, not proof of proportionality at every angle or approval to exceed the catalog travel. The 90° free position and 90° rated deflection describe different aspects of the same example.

Torque differs from force: M = Fr for perpendicular force at radius r; generally M = Fr sin β, where β separates the radius and force directions. Derived using the example's rounded R = 0.188 in, 0.050 lbf·in gives 0.266 lbf perpendicular force. This uses tabulated R, not A/2 = 0.1875 in. Changing contact radius changes force. Lee, torque terminology.

The suggested mandrel belongs to the catalog geometry and travel. Loaded bore, axial growth and friction remain assembly-specific. Lee, design considerations.

Source dates and qualification limits

Retrieved 2026-10-31 PDT: Lee prints 2019 Product Catalog and ©2019. The 2019-07 URL differs from PDF timestamps: creation January 4, modification July 18, 2019. Timestamps are not a printed revision. Lee catalog, cover and back cover.

Newcomb's single-page Torsion Springs sheet has no printed edition/date; its PDF metadata records April 24, 2013. The cited engineering web pages have no displayed article revision date. Two guessed Newcomb torsion-specific resource URLs were inaccessible through web retrieval; the working helical-spring resource URLs were followed from its actual resource index. No inaccessible text supplies a claim here.

Full SMI handbooks and ASTM standards were not read. Manufacturer references to them do not establish independent standards verification. The Lee values describe a named catalog reference, not a current purchased lot. No customer assembly, cycle spectrum, temperature exposure, corrosion condition, fatigue life or preload was tested. Catalog ratings and the worked calculations establish no universal installation, life guarantee or customer qualification.

Production planning references.