Two load points, one spring: designing variable pitch without trial and error

A classic progressive compression spec looks like this: 13.5 N compressed to 23 mm and 48.7 N compressed to 19 mm. Two points, with a rate change between them. No uniform-pitch spring satisfies both at once: the second segment's rate is higher than the first's.

The physical answer is variable pitch: a run of coils wound closer together that lands first. While every coil works, the spring is soft. Once the tight zone stacks coil against coil, only the open coils remain and the rate rises. The load curve gains a knee, and that knee is exactly what lets you hit both points.

Why solving by hand hurts

The traditional flow is iterative: guess a coil split, guess a pitch for the tight zone, compute the load at the second point, compare, nudge the pitch, recompute. Every round moves the knee and shifts the result. Spending half an hour of trial and error to land the second load is common, and any spec revision resets the work.

Worse: the problem has no unique answer. Infinitely many combinations of coil split and pitch pass through the same two points. Hand-solvers usually stop at the first one that closes, with no idea whether it is a good spring.

What the solver does

In our studio you state the two points (load and length for each) and the calc engine resolves the rest in closed form.

• The first-stage rate pins the active coil count: it falls straight out of the spring-rate formula.
• For every possible split between tight and open coils, the second-stage rate is forced, and the transition point that makes the second load land has an exact solution.
• Each candidate is validated by the same engine that computes everything else in the studio: manufacturing limits, solid height, minimum and maximum pitch.

The solution family and the pick criterion

Since the problem admits a family of answers, the solver presents the best ones and recommends one on an explicit criterion: the lowest stress when the spring goes to solid. Fewer open coils means more stress concentrated in them at the end of travel; the balanced solution spreads the work and keeps the most fatigue margin.

You see the alternatives with their numbers (total coils, tight coils, pitch, stress at solid) and apply the one you prefer. The spring updates in 3D instantly, with the load curve showing the knee in the right place.

From spec to quote

Because the solver lives inside the same tool that computes price, tolerances and machine time, the path from a two-load spec to a quote is continuous: solve, check the curve, quote. What used to be an afternoon of iteration becomes a minute of review.