# Compression springs

Helical compression-spring geometry, force and rate, end contact, and the limits of a bounded catalog example.

Reviewed: 2026-10-31

Tags: components, mechanical, springs

Gutekunst **D-102** lists **12.50 mm** free length, **5.40 mm** minimum static length and **2.334 N/mm** rate. The nominal **7.10 mm** deflection gives **16.5714 N**, close to the catalog's **16.58 N** static endpoint using rounded inputs. Check solid height, guidance and fatigue separately for cycling. [D-102 product table](https://www.federnshop.com/en/products/compression_springs/d-102.html).

## Identity and axial load path

A compression spring shortens under axial load. In a cylindrical round-wire spring, the body wire primarily carries torsion. The seats determine how the force enters the end coils. [Lee Spring, Compression Springs](https://www.leespring.com/learn-about-compression-springs), [W.B. Jones, Compression Springs Information](https://www.springsfast.com/products/compression-springs/compression-springs-information/).

Free length is unloaded length. Axial deflection is the difference from working length. Solid height describes touching coils, while permanent set remains after unloading. [Lee Spring glossary](https://www.leespring.com/technical-glossary).

## Wire, coils and rate

For round wire, `d` is wire diameter and `D` is mean coil diameter, measured through wire centers. Outside and inside diameters satisfy `Do = D + d` and `Di = D − d`; spring index is `C = D/d`. Pitch is axial distance between corresponding points on successive turns, whereas clear gap excludes wire thickness. Active coils contribute to deflection; total coils also include inactive end turns. End construction determines their relationship. [Maruho Spring, Calculation of Compression Coil Springs](https://www.maruho-htj.co.jp/en/mnet/design/compression/); [Lee Spring glossary](https://www.leespring.com/technical-glossary).

For an idealized cylindrical round-wire spring in its elastic, approximately linear range:

```text
k = G d^4 / (8 Na D^3)
F = k δ = k (L0 − L)
k = (F2 − F1) / (L1 − L2)
```

Here `Na` is active-coil count, `G` is shear modulus in N/mm², dimensions are mm, force is N and rate `k` is N/mm. The two-height expression assumes `L1 > L2` and corresponding `F2 > F1`. Larger wire increases calculated stiffness strongly; larger mean diameter or more active coils decreases it, with the other inputs fixed. These are model relationships, not independent manufacturing adjustments. Maruho notes that larger pitch and small active-coil counts can cause departures from the basic calculation. [Maruho, formulas 1–3 and 8, design considerations](https://www.maruho-htj.co.jp/en/mnet/design/compression/).

A spring installed below free length has a preload under that model. Preload is a force at a particular installed height, not a universal percentage of free length. A catalog rate alone does not determine force without a reference length and displacement. This is explanatory synthesis of the preceding relationships.

## End forms, seating and coil contact

Open ends retain the helix near the tip; closed or squared ends reduce end pitch so adjacent end turns touch. Grinding creates bearing faces. The four basic combinations are open, open and ground, closed, and closed and ground. They change seating, total-versus-active turns and solid height. Newcomb gives nominal solid-height relations of `Nt × d` for ground ends and `(Nt + 1) × d` for unground ends, where `Nt` is total turns. Finish and manufacturing tolerances affect actual stacked height; these expressions do not establish an allowable working stroke. [Lee Spring glossary](https://www.leespring.com/technical-glossary); [Newcomb Spring, Solid Height](https://www.newcombspring.com/resources/compression-spring-solid-height).

Constant rate is an approximation over an interval. W.B. Jones describes lower initial stiffness while the ends seat and rising stiffness near the end of travel as coils progressively contact. Consequently, `F/δ` from the free position can differ from a measured two-point slope. Coil bind removes the intended elastic travel; it does not create a larger useful range of the original rate. [W.B. Jones, End Coil Effects](https://www.springsfast.com/products/compression-springs/compression-springs-information/).

## Bounded example: Gutekunst D-102

Gutekunst's **D-102** compression-spring data sheet, **printed 10.2026, page 1 of 1**, identifies drawn EN 10270-1 wire, right-hand coiling and closed, ground ends. It gives the following values. Decimal commas in the sheet are rendered here as decimal points. [D-102 manufacturer PDF](https://www.federnshop.com/en/data-sheet/federnshop-data-sheet-compression-spring_d-102.pdf).

| Property | Sheet value |
| --- | --- |
| Wire `d`; mean diameter `D` | 0.63 mm; 5.00 mm |
| Outside diameter `De` | 5.63 ± 0.20 mm |
| Free length `L0` | 12.50 ± 0.44 mm |
| Active turns `n`; rate `R` | 5.50; 2.334 N/mm |
| Static maximum force `Fn` at minimum static length `Ln` | 16.58 ± 1.27 N at 5.40 mm |
| Maximum static deflection `sn` | 7.10 mm |
| Mandrel diameter `Dd`; bush diameter `Dh` | 4.00 mm; 6.10 mm |

The surface-treatment field is blank and its shot-peened box is unchecked; no coating or shot-peening is established. Total turns, block length and theoretical block force are blank. The sheet's dynamic values apply only to a shot-peened hardened surface; they therefore do not establish dynamic capability for this depicted condition. [D-102 PDF, p. 1](https://www.federnshop.com/en/data-sheet/federnshop-data-sheet-compression-spring_d-102.pdf).

The separate live [D-102 product table](https://www.federnshop.com/en/products/compression_springs/d-102.html) gives `Fn = 16.576 N`, rather than the PDF's rounded 16.58 N. Its listed static minimum length is 5.4 mm and rate is 2.334 N/mm. It leaves application preload and loaded-height fields empty; those are not zero-valued operating requirements.

**Derived arithmetic:** at the catalog static endpoint, nominal deflection is `12.50 − 5.40 = 7.10 mm`. Multiplying `2.334 N/mm × 7.10 mm = 16.5714 N` approximately reproduces the tabulated force; rounded catalog inputs do not give exact equality. At an illustrative **10.00 mm** working length, the same constant-rate model gives `δ = 2.50 mm` and `F ≈ 5.835 N`. This is a calculated illustration, not a manufacturer force test at 10.00 mm. The cited force tolerance belongs to `Fn`; it does not establish a tolerance at this illustrative height. The sheet supplies no independent rate tolerance or covariance between length and force errors. Neither calculation establishes fatigue life or margin to solid height.

## Stress, stability and time-dependent limits

For round-wire helical springs, Newcomb gives corrected torsional stress as `τ = Kw × 8FD/(πd³)`, where the elastic Wahl factor is `Kw = (4C − 1)/(4C − 4) + 0.615/C`. With N and mm, stress is N/mm² (MPa). Curvature and direct shear make stress uneven, with the maximum at the inside of the coil. Newcomb distinguishes correction conventions after yielding or at elevated temperature: an allowable-stress comparison depends on the convention used to establish the reference data. This equation is not itself a permissible-stress rule. [Newcomb Spring, Compression Spring Stress, attributed to SMI](https://www.newcombspring.com/resources/compression-spring-stress).

Buckling is lateral instability of the compressed spring axis; end restraint and slenderness influence it. A guide rod or surrounding hole introduces mating clearances as well as guidance. Lee notes that the bore must accommodate spring outside-diameter tolerance and expansion during compression. A nominal diameter match alone does not demonstrate freedom from rubbing or binding. [Lee Spring glossary](https://www.leespring.com/technical-glossary); [Lee Spring, key parameters](https://www.leespring.com/learn-about-compression-springs).

Relaxation is force loss with time at fixed deflection; creep is length change with time at constant force. Relaxation depends on stress, temperature and duration. Fatigue concerns repeated or fluctuating stress and can occur below the elastic limit. A single static force rating therefore cannot establish cycle life, long-term retained force or stability in a specific assembly. [Lee Spring glossary](https://www.leespring.com/technical-glossary).

Application qualification remains specific to installed heights, force range, temperature and dwell time, loading frequency, environment, seating and guidance, material condition and required life. This is engineering synthesis, not a universal selection, preload, installation or stress limit.

## Evidence scope

Sources were accessed **2026-10-31 PDT**. The directly downloaded and visually read D-102 PDF carries **10.2026**; the search service returned a cached extraction marked **01.2026**, and an earlier search snippet marked **03.2026**. The October document is the bounded example here. The initial direct PDF request returned HTTP 403; a subsequent request succeeded. W.B. Jones's text was readable through the search service, while direct capture encountered an access challenge. These access differences do not establish a revision history.

The cited HTML references have no identified edition or substantive revision date. Their copyright dates are not treated as technical editions. The full DIN, EN, ISO and JIS standards mentioned by the manufacturers were not read; no standard-wide compliance or tolerance interpretation is claimed. No customer spring, lot certification, test history, operating temperature, environment or life requirement was supplied. This reference does not establish customer capability or approval.