Engineering tools
Coiling Calculator — Instructions & Guide
How to use the trapezoidal wire preform calculator, what each field means, and a worked example.
What this calculator does
When wire is coiled into a ring of rectangular cross-section, the wire itself must start as a trapezoidal preform — the inner edge of the coil travels a shorter path than the outer edge, so a rectangular section would distort into a trapezoid once bent. This tool works the problem backwards: starting from the rectangular ring you want to finish with, it calculates the trapezoidal preform dimensions your wire profiling needs to produce before coiling.
It is built on elastic-plastic bending theory, with a set of optional corrections you can switch on for springback, Poisson effects, thermal expansion and process-specific behaviour at the coiling head.
Basic inputs
| Field | Meaning |
|---|---|
| Outer Diameter, DOD | The outer diameter of the finished ring, in mm. |
| Radial Thickness, T | The radial wall thickness of the finished rectangular section, in mm. |
| Final Rectangular Width, W | The axial width of the finished rectangular wire section, in mm. |
| Neutral Axis Shift, ΔR | Manual offset to the neutral bending radius, if known from experience or measurement. Leave at 0 if unsure. |
These four values alone will give you a baseline preform calculation. Everything below is optional refinement.
Material properties & process parameters
Selecting a Material Type from the dropdown auto-fills typical Elastic Modulus (E), Yield Stress (σy) and Poisson's Ratio (ν) for that material. You can override any of these manually — useful if you have mill-certified or measured values for your actual wire batch, which will always be more accurate than generic typical values.
Operating Temperature only affects the result if "Enable Thermal Effects" is switched on (see below). Coiling Speed and Coiling Tension only affect the result if "Enable Process-Specific Corrections" is switched on.
Advanced physics corrections
| Toggle | What it adds | When to use it |
|---|---|---|
| Poisson Effect Correction | Accounts for the wire trying to widen on the inner (compressed) edge and narrow on the outer (stretched) edge during bending. | Worth enabling for most jobs — it's a real and usually significant effect. |
| Thermal Effects | Adjusts modulus, yield stress and adds thermal expansion strain based on Operating Temperature. | Enable if coiling happens significantly above or below room temperature (e.g. heated dies, hot forming). |
| Non-linear Strain Distribution | Replaces the simple linear strain assumption with an elastic-plastic model — more accurate for tight bend radii where the material is well into plastic deformation. | Enable for tight coils (low R/T ratio) or higher-strength materials. |
| Process-Specific Corrections | Applies empirical adjustments for coiling speed and tension, and for thin/high-aspect-ratio sections that are harder to form accurately. | Enable once you have a sense of your actual line speed and tension settings. |
Springback Factor (Ksb) and Work Hardening Exponent (n) are tuning parameters for the springback correction, which is always applied. The defaults (1.0 and 0.15) are reasonable starting points for spring steel; adjust them if you have calibration data suggesting otherwise.
Calibration
If you've run a trial coil and measured the actual inner and outer preform widths produced, enter them in Measured Win and Measured Wout. The calculator will blend the theoretical result with your measured values, weighted by the Calibration Gain (0 = ignore measurement, 1 = trust measurement completely, 0.5 = even blend). This is the fastest way to tune the tool to a specific machine and material combination over a few trial runs.
The Machine ID field and "Save Calibration" button log calibration data to the browser console for your own reference — nothing is sent anywhere or stored on our servers.
Reading the results
| Output | Meaning |
|---|---|
| Win / Wout | The required preform widths at the inner and outer edges — this is what you set your wire profiling to produce. |
| ΔW / α / AR | The width difference, the resulting taper angle, and the aspect ratio (width ÷ thickness) of the section. |
| Rm,eff | The effective mean bending radius used in the calculation, after springback correction. |
| ρ / εy | Plasticity ratio and yield strain — useful diagnostic values for understanding how hard the material is working. |
| Confidence | A rough internal estimate (30–95%) of how reliable the result is likely to be, based on geometry ratios and whether calibration data was supplied. Treat this as a guide, not a guarantee. |
| R/T ratio warnings | Flags if the bend is very tight (R/T < 5) or the section is thin and wide (aspect ratio > 5) — both cases where forming is harder to predict accurately. |
Worked example
Using the calculator's default values: DOD = 31.50 mm, T = 1.50 mm, W = 2.50 mm, spring steel selected (E = 210 GPa, σy = 1600 MPa, ν = 0.30), with Poisson correction and non-linear strain distribution both enabled.
This produces preform widths of roughly Win ≈ 2.3 mm and Wout ≈ 2.7 mm — meaning the wire profiling needs to taper from about 2.3 mm to 2.7 mm across the radial thickness before coiling, so that once bent into the 31.5 mm OD ring, the finished section comes out as a true 2.50 mm rectangle. Try it yourself on the calculator page with the default values loaded to see the live figures and the taper angle they produce.
Disclaimer
This calculator is provided free of charge and on an as-is basis, with no warranty or guarantee of accuracy, fitness for purpose, or suitability for any specific application or material.
It is intended as an engineering aid to support, not replace, qualified engineering judgement, proper validation against real production trials, and your own design and quality assurance processes. Forming behaviour varies by material batch, tooling condition, machine setup and many factors this calculator cannot account for.
AbarTech Ltd accepts no liability for any loss, damage, scrap material, downtime or other outcome arising from use of this tool or reliance on its results. By using this calculator you accept that all results are estimates only, requiring independent verification before being relied upon in production.
If you'd like engineering support applying this to a specific job, material or production line, get in touch — we're happy to help directly.