MEC-40

Wahl spring factor

Helical-spring curvature and shear.

Reading speed

MachinesWahl spring factor

Governing equation

K=\frac{4C-1}{4C-4}+\frac{0.615}{C}

$C \in \left[4, 16\right]$

where

C: Spring index (—)
K: Wahl K (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

K=\frac{4C-1}{4C-4}+\frac{0.615}{C}

$C \in \left[4, 16\right]$

$C = 4$ $K = 1.404$

Along the curve

②

Domain of the variable — blue

C_{\min} = 4,\quad C_{\max} = 16

$C \in \left[4, 16\right]$

$C = 4$ $C = 4$

Along the curve

③

Response curve — green

K=\frac{4C-1}{4C-4}+\frac{0.615}{C}

$C \in \left[4, 16\right]$

$C = 4$ $K = 1.404$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}K}{\mathrm{d}C}

$C \in \left[4, 16\right]$

$C = 4.075$ $K^{\prime} = -0.116$

Along the curve

Lecture brief

Historical brief

Machine design grew from Coulomb torsion and Hertz contact (1881) through Soderberg fatigue and the heat-engine cycle. The lab writes shaft, bearing, contact and thermodynamic limits in SI. This sheet (MEC-40 — Wahl spring factor) is the form associated with Wahl spring factor. Working symbols: $C$ $\rightarrow$ $K$ . Helical-spring curvature and shear. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

K

from

C

in Mechanical via

K=\frac{4C-1}{4C-4}+\frac{0.615}{C}

Helical-spring curvature and shear. Use it when a real mechanical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

C = 8.000\,\mathrm{—}

, the governing relation

K=\frac{4C-1}{4C-4}+\frac{0.615}{C}

yields

K = 1.184\,\mathrm{—}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Spring index C8 —

Outputs

Wahl K K1.184 —

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Helical-spring curvature and shear. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube