How a return spring eats your usable stroke

Why this happens

A return spring looks like a fixed subtraction from the solenoid’s force. It is not, and the mistake is treating two curves as two numbers.

The spring is a straight line and the magnet is a curve. A compression spring produces a force that rises linearly as it is compressed. The solenoid produces a force that rises steeply as the air gap closes, roughly as the inverse square of the gap in the unsaturated region and more slowly once the pole faces approach saturation. Laid on the same axes, the spring climbs gently from start to finish while the magnetic curve climbs steeply and then flattens. Over a 4 mm stroke the spring force might change by 0.5 N while the magnetic force changes by more than 4 N. The force actually available to move the load is the difference between them, and that difference has a minimum somewhere along the stroke.

That minimum is not always where people expect it. The conventional picture is that the worst case sits at the end of stroke, where the spring is at its stiffest. That is true when the magnetic curve is still climbing steeply at that point. But when the pole faces approach saturation, the magnetic force stops climbing much, while the spring keeps rising at the same rate, so a second and lower minimum can appear near the end. A well-designed unit has to be checked at both ends and at the crossing in between, because the two minima come from opposite mechanisms and have different fixes. A design that is comfortable at 60 % of stroke can still be negative at 10 % and again at 95 %.

The mechanism with the largest effect is pre-load rather than stiffness. Take a 4 mm working stroke where the spring must deliver 0.5 N at the end stop. There are many springs that will do it. Two of them:

Spring	Stiffness	Pre-load at stroke start	Force at end of stroke
A	0.125 N/mm	0 N	0.5 N
B	0.05 N/mm	0.3 N	0.5 N

Identical at the end stop, and 0.3 N apart at the start, which is where the solenoid has the least to offer. Suppose the magnetic curve gives 0.10 N at 4 mm, 0.30 N at 2 mm and 0.80 N at 0.5 mm. Spring A leaves 0.10 N of net force at the start and 0.30 N at the end. Spring B leaves minus 0.20 N at the start: the plunger does not move at all, because the spring is already stronger than the magnet before the stroke begins. The travel only becomes possible once the magnet reaches 0.30 N, which is at 2 mm, so half the stroke has been converted into pre-load and is unusable.

Temperature is almost never the spring’s fault. The elastic modulus of spring steel falls by about 0.02 % per kelvin, so moving from 20 C to minus 40 C makes the spring stiffer by under 2 %. A cold unit that will not release is fighting thickened grease, a stiffened elastomer or a closed cavity acting as a dashpot, not the spring. The complete cold-start picture is set out in why failure starts at low temperature.

Long-term, the spring does change, but slowly. A spring held compressed at an elevated temperature loses force through stress relaxation, typically a few percent over a thousand hours depending on material, initial stress and temperature. On a design where the spring accounts for a third of the force budget, a few percent is not fatal. On a low-power design where the margin is a few tens of millinewtons, it is. That mechanism is separated from the magnetic ones in why force drops after thermal cycling.

Lateral force is the quiet loss. A compression spring is not an ideal axial element. If the ends are not square, or if the free length exceeds roughly four times the mean coil diameter, the spring buckles and delivers a sideways component at the guided surfaces, where it appears as friction rather than as load. A buckled spring can lose 10 % of its axial force into the guide, which on a 0.5 N design is 50 mN spent on rubbing. Friction scatter between units commonly exceeds magnetic scatter, which is why a spring that looks adequate on paper produces a unit that works and one that does not, and the difference is traced to the magnet rather than to the guide.

Check these in order

1. Draw both curves in the same units on the same axes. This is the whole method, and it takes ten minutes. Stroke along the bottom in millimetres, force up the side in newtons, magnetic curve and spring line together. Most spring problems become visible before any arithmetic is done.

2. Separate pre-load from stiffness and write both down. Get the assembled length, the free length and the rate. Compute the force at the start of stroke and at the end of stroke. If the start-of-stroke spring force is more than a small fraction of the magnetic force at the largest gap, the design has a starting problem.

3. Convert the difference into millimetres of lost travel. Find where the magnetic curve crosses the spring line, and measure from there to the end stop. That distance is the usable stroke, and comparing it with the required stroke is the acceptance test. A design that passes on force and fails on travel is common and is not caught by a force calculation alone.

4. Check the compression ratio. Working length between 70 % and 85 % of free length keeps the spring in its linear region. Below that, force rises much faster than the linear estimate predicts and the curve in step 1 is wrong.

5. Check for buckling before blaming friction. Free length divided by mean coil diameter above about four needs a guide rod or a nested spring. A buckled spring converts axial force into a side load, and the side load shows up as inconsistent behaviour between assemblies rather than as a uniform loss.

6. Check the ends. Closed and ground ends give a square seat; a plain closed end does not, and the difference at the first coil is 2 or 3 degrees of tilt that becomes a lateral force at the plunger. On a 0.5 N spring, that tilt is worth a few tens of millinewtons of side load at the guide. On a bore-guided design this is worth checking before changing anything electrical.

7. Measure the release force, energised and de-energised. Release problems are attributed to weak springs far too often. Measure with a gauge: force to move the plunger while energised, then the same measurement immediately after switching off. If the second is close to the first, the spring is not the constraint. Residual magnetism and release behaviour generally are covered in what to do when it sticks after power off.

What actually to change

What the curves show	What to change	Why not the obvious thing
Net force negative at start of stroke	Reduce pre-load, or increase installed length with a softer spring	Buying a stronger solenoid pays for force everywhere, including where there is already enough
Net force lowest at end of stroke	Check whether the pole faces are saturating	Increasing spring stiffness is the wrong direction here
Force adequate but stroke short	Re-specify pre-load, not stiffness	The requirement is travel, and pre-load is what consumes it
Force budget in tens of millinewtons	Account for stress relaxation in the margin	A spring that is 3 % weaker after a year is not a defect, it is a budget item
Two units behave differently	Check buckling, end squareness and guide clearance	Magnetic scatter is usually smaller than friction scatter
Unit will not release when cold	Check grease viscosity and seal stiffness	Spring force barely changes with temperature
Unit will not release when hot	Measure release force, and check residual magnetism	A hot spring is a very slightly weaker spring
Spring visible at solid length in the drawing	Change the spring or the cavity	A spring at solid length is a rigid spacer, not a spring

Two rows in that table deserve a sentence each.

The row about stress relaxation matters most on low-power designs, because the margin there is often the smallest. If the winding is specified at 1 W and the spring accounts for a third of the available force, then a 5 % loss of spring force changes the net force by under 2 %, which is negligible in isolation and not negligible when the total margin is 10 %. The discipline is to hold the margin as a stated number rather than as an impression, and to state which item it was measured against.

The row about solid length is a drawing check rather than a calculation. A spring drawn at or near its solid length in the assembled condition has no reserve, and its force at that state is not given by the rate at all. It is worth verifying on the assembly drawing, because the error is invisible in any calculation that assumes linear behaviour.

When it IS the harder problem

The spring has to satisfy two different jobs at once. It has to return the mechanism against friction and residue, and it has to stay light enough that the start of stroke is passable. Those two requirements pull in opposite directions, and the escape route is to change the mechanism rather than the spring: a lighter return path, a lower-friction guide, a spring that is shorter and stiffer with almost no pre-load, or a two-stage arrangement where the pre-load is taken up by the mechanism and not by the coil. The arithmetic that decides it is the same as in calculating holding force with a real spring load.

The design is a low-power one. When the available force is a few hundred millinewtons and the stroke is several millimetres, the spring stops being a detail and becomes the design. At 0.3 N of available force over a 4 mm stroke, 0.05 N of pre-load is 17 % of the entire budget. At that point the useful questions are what pre-load can be eliminated entirely, whether the return can be gravity or a light leaf instead of a coil spring, and whether the mechanism can be made bistable so that the spring only has to hold a position rather than to be overcome. Topology choice interacts with this directly, and the differences are set out in open frame versus tubular solenoids.

The requirement is stated as force at end of stroke only. This is the most common specification defect in the whole area, and it is worth naming. Force at end of stroke says nothing about whether the unit will start moving, and a spring chosen to satisfy it can make the unit unable to move at all. The productive move is to re-state the requirement as force available over the whole stroke with the spring in place, or as a required travel that the unit must complete against the stated spring, and then to test the part against that. If the customer cannot state the spring, ask for the mechanism drawing. A force-stroke requirement without the spring it works against is half a requirement, and reading curves that arrive in that state is covered in what a force versus stroke curve leaves out.