Introduction
Springs are among the most commonly used mechanical elements in machine design, yet their selection and design is an area where many engineers underestimate the detail required for reliable performance. Choosing the wrong spring rate, failing to account for fatigue life, or neglecting the effect of stress relaxation at elevated temperatures can produce failures that are expensive to diagnose and difficult to fix after the machine is built. This article covers the design and selection fundamentals for the three most common spring types used in industrial machinery: compression springs, extension springs, and torsion springs.
Compression Spring Design Fundamentals
The compression spring is the most widely used spring type. Its primary design parameters are:
- Spring rate (k): Force per unit deflection, in N/mm. k = Gd⁴ / (8D³Na), where G is the shear modulus of the wire material, d is the wire diameter, D is the mean coil diameter, and Na is the number of active coils.
- Spring index (C = D/d): The ratio of mean coil diameter to wire diameter. Recommended range is 4 to 12. Below 4, manufacturing is difficult and stress concentration is high. Above 12, the spring is prone to buckling and tangling.
- Solid height (Ls): The height of the spring when fully compressed. Ls = Nt × d, where Nt is the total number of coils. The design must ensure the spring never reaches solid height under maximum deflection — a minimum clash allowance of 10–15% of free length is standard practice.
- Buckling: Long, slender compression springs can buckle under load. The critical buckling ratio (free length / mean coil diameter) should be checked. Springs with free length / mean coil diameter greater than approximately 4 are at risk and should be guided by a rod or housed in a cavity.
Wahl correction factor (KW) accounts for curvature and direct shear stress in the coil: KW = (4C–1)/(4C–4) + 0.615/C. The corrected shear stress at the inner fiber of the coil is τ = KW × 8FD / (πd³), where F is the applied load. This corrected stress is used for fatigue life assessment.
Extension Spring Design Specifics
Extension springs differ from compression springs in two important respects: they carry initial tension, and they have formed or coiled end hooks that are stress concentration points.
- Initial tension: Extension springs are wound with the coils in contact, creating a pre-tension that must be overcome before any deflection occurs. The initial tension value is a manufacturing variable that must be specified and verified for critical applications. Typical initial tension ranges are provided by spring manufacturers as a function of spring index.
- End hooks: Standard twisted or hinged end hooks are convenient but are the most common failure point in extension springs. The hook represents an abrupt change in geometry and a point of high bending stress, typically at the inside of the bend where the hook transitions to the coil body. For fatigue-loaded applications, specify reduced-stress hooks (side hooks, extended hooks, or swivel eyes) rather than standard twisted hooks.
- No inherent stop: Unlike compression springs, extension springs have no inherent limit to extension — they can be pulled until they yield or fracture. The design must incorporate a mechanical stop that prevents the spring from being loaded beyond its maximum working load.
Torsion Spring Design
Torsion springs resist rotational deflection and apply a torque rather than a linear force. The spring wire is in bending, not torsion, during loading — an important distinction for stress calculations.
- Spring rate: In N·mm per degree: k = Ed⁴ / (3667 D Na), where E is the elastic modulus (bending), d is wire diameter, D is mean coil diameter, and Na is number of active coils.
- Stress during loading: The bending stress at the inner fiber of the coil, corrected for curvature: σ = KB × 32M / (πd³), where M is the applied moment and KB is the curvature correction factor (inner fiber).
- Coil clearance reduction: As a torsion spring winds up under load, the coil diameter decreases if it is wound in the direction of loading, or increases if wound against the loading direction. The design must account for this diameter change to prevent binding on a guide rod or contact with a housing bore.
Material Selection and Fatigue Considerations
Spring material selection is driven by the operating environment and the duty cycle:
- Patented and drawn carbon steel wire (e.g., JIS SWC, SWB): Most economical, good fatigue strength for static and moderate-cycle applications. Not suitable for temperatures above approximately 120°C or corrosive environments without coating.
- Hardened alloy steel wire (e.g., SWP, SWO): Higher strength than carbon steel, better for higher cycle applications and slightly elevated temperatures.
- Stainless steel (SUS304, SUS316): Good corrosion resistance, moderate temperature capability to approximately 200°C. Lower fatigue strength than carbon steel wire of equivalent diameter — size accordingly.
- Silicon chrome alloy steel: Best fatigue performance for high-cycle applications, suitable to approximately 250°C. Used in automotive valve springs and other high-demand applications.
For fatigue-loaded springs, the design stress at maximum load should not exceed the fatigue limit for the material and stress ratio. Shot peening the spring after coiling significantly improves fatigue life by inducing favorable compressive residual stresses at the wire surface.
Summary Table
| Spring Type | Wire Stress Mode | Key Design Constraint | Common Failure Mode |
|---|---|---|---|
| Compression | Torsion | Solid height / clash allowance | Fatigue at maximum stress coil; buckling |
| Extension | Torsion (body); Bending (hook) | Hook stress; no mechanical stop | Hook failure; over-extension |
| Torsion | Bending | Coil diameter change under load | Inner-fiber fatigue; binding on guide |
FAQ
Q: How do I specify a spring when I know the required load at two positions but not the geometry?
Define the required force at two positions (F1 at position 1, F2 at position 2) and the available envelope (maximum outside diameter, maximum free length). From these constraints you can calculate the required spring rate k = (F2 – F1) / (position2 – position1), and then work backward through the spring rate formula to find a combination of wire diameter, coil diameter, and active coil count that fits within the envelope. Catalog spring tables sorted by rate and outside diameter are useful for this reverse lookup.
Q: When does stress relaxation become a significant concern?
Stress relaxation — the permanent loss of load in a spring held at constant deflection — becomes significant above approximately 100°C for carbon steel springs and above approximately 200°C for silicon chrome alloy springs. If your application operates at elevated temperature with the spring under sustained load, test for relaxation under representative conditions before finalizing the design, and size the initial preload to account for the expected relaxation over the service life.
Q: Can I use a spring in both compression and extension?
A spring designed and manufactured as a compression spring should not be used in extension — it has no end attachment points and the end coils are ground flat for compression seating, not for tension retention. If a single element must work in both directions, use a tension-compression spring specifically designed for bidirectional loading, or use separate compression and extension springs in a back-to-back arrangement.
コメント