Key takeaways
- Contact force at the working deflection is the design target, not the force at a flat position.
- Beam stiffness rises with the cube of thickness, so a small gauge change moves the force far more than a small length change.
- Bending stress at the root decides whether the spring takes a permanent set, and it has to be checked at the maximum deflection.
- Plating, contact resistance and stress relaxation all change the force that actually arrives at the interface.
The force chain in a stamped contact
A stamped contact spring is a beam that pushes a contact surface against a mating surface. The force at the tip has to be high enough to break through surface films, hold the interface closed against vibration and keep the contact resistance stable. It also has to be low enough that the mating part and the housing can accept the reaction without moving.
The force is not a single number. It depends on the deflection at the working position, the beam geometry, the material modulus and the support condition. A spring that measures well at the bench may sit at a different deflection once it is clipped into the housing, because the clip changes the effective length and the root fixity.
The design therefore starts with the working deflection and the required force, then works back to a geometry.
The cantilever model
Most stamped contacts behave like a cantilever beam with a load at the free end. The tip force for a given deflection is three times the modulus times the second moment of area times the deflection, divided by the cube of the beam length. The second moment of area for a rectangular section is the width times the thickness cubed, divided by twelve.
Substituting the section gives a force that rises linearly with width, with the cube of thickness and with deflection, and falls with the cube of length. Thickness is the strongest lever, length is the second, and width is the weakest.
The model assumes a fixed root, a straight beam, a small deflection and a material that stays elastic. A real stamped contact has a curved root, a tapered beam or a formed tip, and the deflection may be a significant fraction of the length. Treat the formula as a sizing tool, then confirm the force on a real part.
A worked example in phosphor bronze
Take a phosphor bronze contact with a modulus of about 110 GPa, a width of 2.0 mm, a thickness of 0.30 mm, a beam length of 8.0 mm and a working deflection of 0.5 mm. The second moment of area is 2.0 times 0.30 cubed divided by 12, which is 0.0045 mm to the fourth.
The tip force is three times 110,000 MPa times 0.0045 times 0.5, divided by 8.0 cubed. That gives about 1.45 N. The root bending stress is six times the force times the length, divided by the width times the thickness squared, which gives about 387 MPa.
Those numbers are illustrative, but they show the scale. A contact force of about 1.5 N is plausible for a small signal contact, and a stress of about 387 MPa is a significant fraction of the yield strength of a spring temper phosphor bronze. If the yield strength at temperature is 550 MPa, the working stress is about 70 per cent of yield, which is high for a contact that must hold force for years.
| Line | Value | Relation |
|---|---|---|
| Modulus, E | 110 GPa | Material property, check at temperature |
| Width, b | 2.0 mm | Stamped outline |
| Thickness, t | 0.30 mm | Strip gauge, confirm mill tolerance |
| Beam length, L | 8.0 mm | From root to contact point |
| Deflection, delta | 0.5 mm | Working position minus free position |
| Second moment, I | 0.0045 mm4 | b times t cubed divided by 12 |
| Tip force, F | About 1.45 N | 3EI delta divided by L cubed |
| Root stress | About 387 MPa | 6FL divided by b t squared |
Illustrative only. Confirm the modulus, yield strength and temper for the actual material lot.
Stress, yield and permanent set
The root of a cantilever carries the highest bending stress. If that stress exceeds the yield strength at the working temperature, the spring takes a permanent set and the force drops. A small set is enough to change a contact force by a noticeable amount, because the free position moves and the working deflection falls.
The safe working stress depends on the material and the duty. A phosphor bronze or a beryllium copper spring can run at a higher fraction of yield than a brass or a soft copper contact. A spring that is deflected once during assembly has an easier life than one that flexes on every mating cycle. The drawing should say which case applies, because the allowable stress is different.
Temperature reduces the yield strength and accelerates relaxation. A contact that runs warm needs a larger margin, checked against the yield strength at the maximum ambient.
Check stress at the maximum deflection, not the nominal
The assembly may over-travel the contact, and a tolerance stack can push the deflection above the drawing nominal. The root stress at that maximum is the one that decides whether the spring takes a set.
Geometry trade-offs
If the force is too low, the instinct is to shorten the beam. That raises the force, but it raises the stress at the same time and reduces the deflection range. Thickening the strip raises the force much faster, because of the cube, and raises the stress even faster. Widening the beam raises the force and lowers the stress, but it takes space and may not fit the housing.
A tapered beam is a common compromise. The root is wider than the tip, which lowers the root stress for the same tip force and uses the material more efficiently. A formed rib along the beam adds stiffness without adding width. A curved beam can give a more constant force over the deflection range, which is useful when the mating surface position varies.
The contact tip geometry matters too. A radiused tip gives a defined contact point and reduces the chance of the tip digging into the mating surface. A flat tip spreads the contact but is more sensitive to alignment. The tip is part of the spring, not a cosmetic detail.
Plating and contact resistance
The force at the tip is only useful if it produces a stable contact resistance. A tin-plated contact needs enough force to break the oxide and hold the soft tin in contact. A silver-plated contact has a lower resistance but can tarnish, and the force has to keep the tarnish film broken. A gold contact is reserved for low-level signals and a high cycle count.
Plating also changes the geometry. A coating adds thickness, which slightly stiffens the beam and changes the tip height. On a thin contact, a plating thickness at the top of its range can move the working deflection enough to matter. If the force is sensitive, specify the plating thickness and check the force after plating.
Contact resistance is not a fixed property of the material pair. It depends on the real contact area, the force, the surface finish and the environment. A force that is adequate on a clean bench sample may not be adequate after a thermal cycle or a vibration test. Test the interface in the condition it will see.
Verification and the drawing
Measure the force at the working deflection on a production sample, not on a hand-formed coupon. Record the free position, the working position and the force. If the force is low, check the free position first: a spring that has taken a set will sit closer to the working position and give a lower force even though the geometry is correct.
Add a load test at the maximum deflection if the contact can be over-travelled. Add a thermal soak if the part runs warm, then re-measure the force. For a part that flexes on every cycle, add a cycling test and check the force at the end, not just the absence of a crack.
On the drawing, give the material and temper, the thickness, the free position, the working deflection and the force at that deflection. Give the contact plating and the maximum contact resistance. A stack of linear dimensions without a force call tells the supplier how to make the shape but not what the shape has to do.
- Material, temper and thickness with tolerance
- Free position and working deflection
- Force at the working deflection, with a tolerance
- Maximum stress or a load test at over-travel
- Contact plating and maximum contact resistance
- Thermal soak or cycling requirement if applicable
Frequently asked questions
How do I calculate the force of a stamped contact spring?
For a cantilever, force equals three times the modulus times the second moment of area times the deflection, divided by the beam length cubed. The second moment for a rectangle is width times thickness cubed divided by twelve. Confirm the result on a real part, because the root and tip are not ideal.
What contact force is enough?
It depends on the plating, the current, the environment and the mating surface. A small signal contact may work at around 1 N, while a power contact needs more. The force has to break the surface film and stay above the minimum after relaxation and thermal cycling.
Why does my contact force drop after assembly?
The assembly may over-travel the spring and cause a permanent set, or the clip may change the effective beam length. Check the free position before and after assembly. If the free position has moved, the spring has yielded and the geometry or the material needs more margin.
Does plating change the spring force?
It can. Plating adds thickness, which slightly stiffens the beam and changes the tip height. On a thin contact the effect can be enough to matter. Specify the plating thickness and measure the force after plating, not only on the bare part.
Sources and further reading
- ASTM B103, Copper alloy plate, sheet, strip and rolled bar
- EN 13601, Copper and copper alloys, rod and wire for electrical purposes
- Qumek contact force and stress reviews for stamped springs
Qumek Engineering Desk
Engineering team
The engineering team behind Qumek drawings, DFM notes, tolerances and inspection standards. Every guide is reviewed against the drawings and processes used on live programmes.
Check the force before the tool is cut
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