Rotary vs. push-pull solenoids: reading a torque-angle curve

Why this happens

A push-pull solenoid has a force-stroke curve. A rotary solenoid has a torque-angle curve, and the two are not the same shape from which a single number can be taken. The difference is not marketing: it comes out of the geometry, and it changes what has to be checked.

Push-pull torque falls monotonically as the gap opens. Force rises as the plunger approaches the pole face, so the power available is greatest exactly where the mechanism is almost finished moving, and least at the start of the stroke where the largest gap has to be crossed. Over a 4 mm stroke the force at the start can be a tenth of the force at the end. That shape is awkward but predictable.

The rotary curve is not monotonic. A typical rotary solenoid works by rotating a rotor between pole pieces, so the area presented to the flux changes with angle. Near the start of the rotation, and again near the end, the geometry is less favourable than it is somewhere in the middle. Torque therefore climbs, peaks, and falls away. On common designs the peak sits somewhere between 40 % and 60 % of the rated rotation, and the torque at the two ends is a fraction of that peak. A datasheet that highlights the peak is quoting the one point on the curve that the mechanism passes through without needing force. A unit rated 0.15 Nm at peak with 40 % available at the end stop is offering 0.06 Nm at the angle where the return spring is stiffest.

The lever changes the units and the sensitivity. Torque is force times radius, so a unit producing 20 N at a lever radius of 8 mm delivers 0.16 N·m. Small rotary units are often specified in the range 0.02 N·m to 0.2 N·m over rotations between 25 degrees and 95 degrees. Two consequences follow. First, everything downstream has to be designed in the same unit, because comparing a torque figure against a force figure is a common and expensive slip. Second, the lever ratio is part of the specification: if the mechanism attaches at 12 mm rather than the 8 mm the curve was taken at, the available force at the point of use falls by a third even though the torque is unchanged.

The return spring changes sign and rises with angle. A torsion spring produces torque that increases roughly linearly with rotation, and it opposes the coil throughout. So the delivered torque is the difference between a curve that arches downwards and a line that climbs. The margin is smallest where the two meet, and on a design with a substantial spring that point is near the end of the rotation, which is exactly where the magnetic torque has already fallen away. A spring that contributes 0.03 Nm at the end of a 60 degree rotation has taken a fifth of the budget if the unit peaks at 0.15 Nm. The general form of this problem is set out in how a return spring eats usable stroke.

The temperature correction is unchanged, and is often forgotten on rotary units. The winding is copper. Resistance rises at 0.393 % per kelvin, so a unit settling 70 K above its measurement temperature draws about 78 % of its cold current at constant voltage, and torque falls to roughly 61 % of the cold curve. Rotary units are frequently packaged in small frames with little radiating area, so they can run hotter than a comparable push-pull design at the same power.

Check these in order

1. Mark the angle range you actually need on the curve. Not the rated rotation, and not the full axis. If the mechanism moves through 40 degrees starting from 15 degrees of pre-rotation, that interval is the only part of the curve that matters, and everything outside it is decoration.

2. Read the minimum torque inside that interval. For most rotary curves that minimum sits at one of the two ends of the interval. Record it, and record which end, because the fix depends on which one it is. On a curve that peaks at 0.15 Nm, the two ends commonly sit between 0.05 and 0.07 Nm.

3. Overlay the spring or load curve in the same units. Convert the load to torque about the same axis before drawing it. A load that is a spring is a line rising with angle; a load that is friction is roughly flat; a load that is inertia is a different shape again. The intersection is the operating point and the gap between the curves is the margin.

4. Confirm the lever radius the curve was measured at. If the supplier worked at 6 mm and the mechanism attaches at 9 mm, available force at the attachment falls by a third. Torque is invariant, force is not, and the customer’s requirement is usually expressed as force at a point.

5. Establish where angular zero is. Some curves start at the mechanically seated position, some at the first position where the coil produces measurable torque. A pre-rotation of 10 degrees moves the working interval along the curve, and near the ends that shift is worth more torque than any other number on the sheet.

6. Look at the holding value rather than the peak. If the mechanism has to remain energised at the end of the rotation, the relevant figure is the torque available at that angle, not at the peak. On a curve that falls to 40 % of peak at the end stop, the thermal budget is being spent on a fraction of the advertised output.

7. Size the end stop for the kinetic energy, not for the torque. A rotor arriving at a hard stop converts its rotational kinetic energy into an impact, and doubling the speed quadruples the energy, so a design that is acceptable at 50 ms per rotation may not be at 25 ms. A rotor with 5 g·cm² of inertia completing 60 degrees in 50 ms runs at about 21 rad/s, which is 0.11 mJ of energy delivered into the stop every cycle. That is small in absolute terms and large in a contact patch: a million operations is 110 J aimed at the same few square millimetres, which is why rotary units seize at the end stop rather than burn out the coil.

8. Check what happens on release. Measure the time to return and the angle actually reached, not just the angle commanded. A 60 degree return that takes 80 ms when new and 200 ms after a winter of cold starts is telling you about the lubricant rather than about the spring. A torsion spring that is adequate to hold the mechanism against gravity may not be adequate to drive it back against friction in a cold, dry environment.

What actually to change

What the curve shows	What to change	Why not the obvious thing
Minimum torque occurs at the start of the rotation	Reduce the starting angle, or pre-load with a lighter spring	Increasing the rated rotation does not change a gap at one end
Minimum torque occurs at the end of the rotation	Reduce the end-of-rotation spring force, or accept a shorter rotation	A larger unit adds torque everywhere, including where it is not needed
Peak torque looks adequate but the unit stalls	Re-read the curve at the minimum, then correct for temperature	The peak is not a working condition
Mechanism applies the load at a larger radius	Recalculate in force, not torque	Torque is preserved by the lever and force is not
Torque collapses at the end stop	Check the pole geometry and the residual gap	The end of a rotary stroke is a geometry limit, not a supply limit
Unit stalls only when warm	Get a hot curve, and check the enclosure’s radiating area	A rotary frame is often a poor heat path
End stop wearing or seizing	Add a compliant stop or reduce the seating velocity	Increasing torque increases the impact energy as well
Position drifts after release	The return spring is not the position reference	An open-loop rotary unit has no inherent position memory

The row about position is worth stating plainly, because it is where rotary units are most often misapplied. A rotary solenoid is an actuator, not a positioning device. It drives to a mechanical stop or against a spring, and the position it reaches is set by the geometry of the mechanism, not by the coil. If the requirement is a repeatable angle that the unit itself defines, no amount of electrical refinement will deliver it, and the mechanism has to supply the reference. Loads acting at an angle rather than along the axis are treated in latch geometry and lock solenoid force.

When it IS the harder problem

The load needs roughly constant torque across the whole rotation. Then no single rotary unit as drawn will do it, because the curve arches away from flat at both ends. Two units arranged so that their torque curves overlap by 50 % sum to something much flatter than either one alone. The workable routes are a mechanism that linearises the output, a two-coil unit designed so that the two torque curves overlap, or a cam profile that matches the load to the shape the unit actually produces. Choosing the unit by peak torque and hoping the ends work out is what produces the classic complaint that the actuator is strong enough in the middle and not strong enough anywhere useful.

The rotation has to be bidirectional. A plain rotary unit drives one way and returns by spring. A mechanism that needs to be driven in both directions needs either two coils arranged to produce opposing moments, a reversing linkage, or a design where the spring is replaced by the second coil. Each of those changes the thermal budget, because the coil that was energised briefly in one direction is now energised in both. A drive specified at 10 % duty in one direction becomes a 20 % duty drive, and the winding settles hotter for it.

The rotation has to be held with the power off. This is a mechanical requirement wearing an electrical costume. A detent, a bistable magnetic circuit or a gear train that does not back-drive will hold position with no current; a plain rotary unit will not hold it with any current you are willing to pay for. The arithmetic on holding is the same as for the linear case, and it is set out in latching solenoid principle and its driving cost.

The unit is being chosen from a curve with no stated conditions. Then the comparison against a competing part is not a comparison at all. Two curves taken at different temperatures, or at different lever radii, will rank the parts in the wrong order, and on a decision that is close the error is large enough to reverse it. Ask both suppliers for torque at their stated angle interval, at a stated winding temperature, at the low end of the supply tolerance, and compare like with like. If they cannot supply it, get a unit from each and measure both on your own rig, in the same fixture, at the same angle, on the same day. For the linear case where the same discipline applies, see reading a force versus stroke curve.