Reading a solenoid force vs. stroke curve: what the datasheet leaves out
A force-stroke curve is one snapshot taken at one temperature, one voltage and on one sample. Add the omissions back and the picture changes: a winding 70 K above ambient costs about 39 % of the force, a 10 % voltage shortfall costs 19 %, and the low end of a batch costs more again. Here is what to ask for, and in what order.
Why this happens
A force-stroke curve is drawn as though it were a property of the part. It is closer to a photograph. It records one sample, at one temperature, at one supply voltage, with the plunger held by a rig whose axial alignment is not recorded. Each of those was a decision, and the decisions are rarely printed beside the line.
Temperature is the largest omission and the shortest piece of arithmetic. Copper resistance rises at 0.393 % per kelvin. A winding that settles 70 K above the temperature it was measured at carries 27.5 % more resistance, so at constant voltage it draws about 78 % of the test current. Force follows the square of current while the circuit is unsaturated, which puts it near 61 % of the published figure. A cold curve is not the curve the machine sees. It is the curve the machine sees in the first seconds of a cold start, and it has already gone by the time the winding reaches operating temperature. The mechanism is worked through in how to calculate holding force.
The second omission is the supply. A 24 V drive specified with a plus or minus 10 % tolerance covers 21.6 V to 26.4 V. At constant resistance force varies with the square of voltage, so the bottom of that band removes 19 % of the force before anything else is considered. Curves are commonly taken at nominal voltage from a laboratory supply that sat exactly there, which is the most favourable point in the range.
The third is the unit itself. Published curves are typical values, and some are single-sample values. Winding resistance, turns count, plating thickness and assembled air gap all vary within a batch. If ampere-turns spread by 5 %, the low end of the batch sits about 10 % down on force. Spread in the assembled gap is more damaging than the same percentage in the winding, because the gap that governs the magnetic circuit includes the mounting face, the plating and any residual shim, not only the dimension on the drawing. Batch behaviour is set out in inconsistent force across a batch.
Multiply the three and the curve changes shape. Take the low voltage end at 0.81, the hot winding at 0.61 and a batch low end at 0.90. The product is 0.44. Add an assembled gap 0.05 mm larger than the drawing, which costs a further 26 %, and a nominal 10 N curve arrives at end of stroke as roughly 3 N. Nothing in that chain is exotic. Every step is a tolerance somebody already accepted somewhere in the programme.
Two more things are missing from most curves, and neither is a tolerance. The first is the stroke datum. A curve that begins at 0 mm assumes the plunger is touching its stop; if the assembly leaves a residual gap of 0.2 mm, the usable part of the curve starts where the working stroke starts, and the final fraction of the published line describes a position the unit never reaches. The second is the measurement axis. If the push rod that drives the load cell is off the plunger axis, the reading includes a bending moment that the real load does not apply, and over a short stroke that biases the result upward.
And the curve frequently stops early. Many published curves end at 2 mm or 3 mm, because the product line was drawn for short strokes. If the requirement is 4 mm, the last millimetre is an extrapolation, and the inverse-square region is precisely where extrapolation is least safe, as the crossover behaviour between topologies shows in open frame versus tubular designs.
Check these in order
1. Ask whether the curve is typical or guaranteed. These are different claims and only one of them can be designed against. If the answer is typical, ask what the spread is and where the lower limit sits. A supplier who cannot answer is telling you the curve came from a single sample.
2. Ask at what temperature it was measured, and whether the winding was at equilibrium. A curve taken in the first 30 seconds of a cold unit is a cold-start curve. A curve taken after the winding has stopped rising is the one that describes steady operation. Both are useful; they are not interchangeable.
3. Ask whether the drive was constant voltage or constant current, and at what value. A constant-current curve does not roll off with temperature, because current is held by the supply. A constant-voltage curve does, and by the factor above. For most equipment the drive is constant voltage, so the constant-current curve overstates what the customer will get.
4. Establish where the stroke zero is. Find out whether the 0 mm point is pole face on pole face, or the position with the mechanism’s stop engaged. An offset of a few tenths of a millimetre moves the whole working window along the curve, and at the steep end of the curve that offset is worth more force than any other single figure on the sheet.
5. Find out how the force was measured. Check the axis alignment and check whether the rig constrains the plunger laterally. A rig that holds the plunger concentric removes friction from the measurement, and that friction returns when the part is installed in its own bore. Off-axis measurement commonly reads 5 % to 10 % high over a short stroke, which is the same order as the batch spread it is being used to judge.
6. Compare the domain of the curve with the working stroke. Overlay the two. If the curve ends before the stroke does, the missing part is an assumption rather than a measurement, and it needs to be established before the design is frozen.
7. Check whether the curve is a pull-in curve, a hold curve, or both. Pull-in is what the unit can do from a standing start at each position. Hold is what it sustains once seated. A curve labelled with a single force figure is normally the peak hold value, which is the least useful number on the page for a mechanism that has to move something.
8. Ask for the sample size behind the curve. One unit is an anecdote. Ten units give a mean and a hint of spread. Thirty give a distribution you can subtract a margin from.
What actually to change
| What the curve says | What to change | Why not the obvious thing |
|---|---|---|
| Force adequate at nominal only | Specify the low end of the supply tolerance and re-read the curve | Buying a higher-rated unit pays for force you may not need |
| Force adequate cold | Get a curve at stabilised winding temperature | Rewinding does not change the temperature coefficient |
| Curve ends before the stroke ends | Have the curve measured over the working range | Extrapolating the inverse-square region is guesswork |
| Force varies unit to unit in your own samples | Characterise the gap before the winding | Winding spread is usually the smaller term |
| Measured force beats the application | Check the rig axis and the lateral constraint | A generous bench result is often a rig artefact |
| Customer rejects parts that pass on the bench | Write the measurement conditions into the drawing | The argument is about test conditions, not about the part |
The last row is where most of these disputes end up, and the fix is a sentence rather than a redesign. A requirement that reads “12 N minimum at end of stroke” is not testable. One that reads “12 N minimum at end of stroke, at a winding temperature of 90 C, at 90 % of rated voltage, on any unit in the batch, with the plunger on axis” can be measured, accepted or rejected, and costed. Writing it that way also exposes which of those conditions is actually expensive, and it is usually the temperature, not the voltage. Mounting-related losses of the same kind are covered in works on the bench, fails in the machine.
When it IS the harder problem
The load is a spring rather than a weight. Then the requirement is the difference between two curves that both vary with position, and neither the peak force nor the force at either end of stroke is the deciding number. The worst case sits somewhere in the middle, and finding it means overlaying the spring line on the force curve. That case is treated in how a return spring eats usable stroke.
The curve was taken on a design that is not the one being built. This happens whenever a supplier quotes a family curve, or when a prototype was made with a hand-wound coil and the production part is machine-wound. A 7 % shortfall in turns count is 14 % of the force, and it shows as a constant offset along the whole curve rather than as scatter. The tell is a consistent offset rather than a random scatter: production sits a fixed percentage below the prototype everywhere along the stroke. That is a design difference, not a tolerance, and it should be resolved by re-measuring rather than by adding margin, because margin added on top of an unexplained offset hides the offset permanently.
The stroke is long relative to the pole face. Beyond roughly the face radius, fringing is no longer a correction but a leading term, leakage grows with the gap, and the shape of the curve stops being predictable from the flat-face expressions. On a 6 mm face that point is 3 mm of stroke, and past it every assumption behind the formula has failed at once. Closed-form arithmetic cannot carry the answer, and this is where finite element analysis earns its cost.
The curve is being used to compare two suppliers. Then the comparison is only valid if the three conditions above match. Two curves taken at different temperatures, or one at nominal voltage and one at minimum, will rank the suppliers in the wrong order, and the error is large enough to reverse a decision that is close. A 10 % voltage difference alone is worth 19 % of the force, which is more than the difference between most competing parts. Ask both for the same conditions, and if they cannot supply it, standardise the comparison on your own test rig with one unit from each. A curve is a measurement, not a specification, and it only becomes a specification when the conditions travel with it.
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Frequently asked
- Why does the solenoid pull less than its published curve says it should?
- Because the curve was almost certainly measured cold, at nominal voltage, on a typical sample. Restore the three conditions that are usually left out and the number falls a long way. A 10 % voltage shortfall costs 19 % of the force, a winding settling 70 K above ambient costs about 39 %, and the low end of a batch with a few percent of spread costs roughly 10 % more. Multiplied, they bring a nominal curve to under half of itself.
- Should I design to the typical curve or to a minimum?
- To a minimum, and the minimum is not printed. A published curve is usually a typical value, sometimes taken from one sample. If ampere-turns vary by 5 % across a batch, the low end sits about 10 % down on force, because force goes with the square of ampere-turns. Variation in the assembled air gap is more damaging than the same percentage in the winding, because the gap that governs the circuit includes the mounting face and the plating, not only the drawing dimension.
- The curve stops at 2 mm but my stroke is 4 mm. Can I extrapolate?
- Not reliably. Most curves stop where the product line stops being useful, and beyond that point the inverse-square behaviour is being modified by fringing, leakage and saturation all at once. Fringing extends the effective pole area by about one gap length around the perimeter, so once the gap approaches the face radius the simple geometry has stopped describing the device. Ask for a curve over the range you actually need, or have it measured.
- How is the force normally measured, and how can that be wrong?
- Usually by pushing the plunger against a load cell at a series of positions. Two things go wrong. If the load cell axis is not aligned with the plunger axis, the reading includes a bending moment the real load does not apply and is biased upward. And if the rig constrains the plunger sideways while the application does not, friction disappears from the measurement and reappears in service.
- What single change most improves a specification built on a curve?
- Write the conditions next to the requirement. Force at end of stroke, at the winding's stabilised temperature, at the low end of the supply tolerance, at the low limit of the batch, with the plunger on axis. A bare force figure cannot be accepted or rejected, because it describes no particular state of the product.