Bolted Joint Contact Resistance Calculator
Two nominally flat surfaces touch only at a handful of microscopic spots. Current squeezes through those, and the resulting constriction resistance is what makes joints run hot. This is Holm's classical treatment: spot size from contact force and hardness, then resistance from spot size.
Choosing something to solve for makes Total joint resistance an editable target and computes the chosen input from it.
Formula
| F | total force pressing the surfaces together (N) |
| n | number of load-bearing contact spots |
| H | Meyer hardness of the softer material (Pa) |
| xi | deformation coefficient, elastic to fully plastic |
| alpha | radius of the cluster the spots occupy (m) |
What this model assumes, and where it stops
Assumptions
- Circular contact spots of equal size, uniformly loaded.
- Fully or partly plastic deformation set by the deformation coefficient.
- Both members are semi-infinite compared with the spot size.
- Any surface film is uniform over the real contact area.
- Isothermal joint - no thermal-electrical feedback.
Limitations
- The spot count is a guess, and the answer scales as one over its square root. Treat the result as an order of magnitude unless you have measured the joint.
- Real contact spots are neither circular, equal, nor uniformly loaded, and the largest few carry most of the current.
- Film resistance is enormously variable, spanning orders of magnitude with age, humidity and temperature. It is also what makes joints degrade over time, which no static calculation captures.
- Aluminium is a special case: its oxide re-forms almost instantly, so joints need mechanical abrasion, inhibitor compound and Belleville washers, none of which appear in this model.
- The force reaching the contact interface is not the bolt preload. Washer geometry and plate stiffness decide the actual pressure distribution.
- Thermal runaway - resistance heats the joint, heat relaxes the bolt, relaxation raises the resistance - is the usual failure mode and is entirely outside this steady calculation.
When you need a 3D field solution instead
Closed-form models like the one above hold on idealised geometry. These are the cases where they stop being good enough and a full 3D electromagnetic and thermal solution is the only way to get a trustworthy answer:
- The actual pressure distribution around a bolt, which sets where contact really occurs and is a contact-mechanics problem.
- Joint temperature, where the loss computed here feeds back into resistance and into bolt preload relaxation.
- Current crowding around the joint, since current has to divert through the contact region rather than flowing straight on.
- Multi-bolt joints, where the bolts share load and current unevenly.
- Dissimilar-metal joints, where differential expansion cycles the contact pressure.
Common questions
What resistance should a good busbar joint have?
A clean, properly torqued bolted joint with about 20 kN of clamping force works out around 1 to 2 microohm in this model - at 630 A that is half a watt, which is negligible. The classical acceptance rule is that a joint should not exceed the resistance of an equal length of plain bar. If a micro-ohmmeter reads tens of microohms, the joint is dirty, loose or corroded, not "normal".
Why do busbar joints fail years after installation?
Films. The same 20 kN joint with a typical oxide film roughly doubles to 2.6 microohm, with the film carrying nearly half the total. More resistance means more heat, more heat accelerates oxidation and creep relaxation of the bolts, and the loop runs away - which is why thermography and periodic retorquing are maintenance staples, and why plating and joint compound exist.
Should I add more bolts or more torque?
What matters is total clamping force, which sets the real metal-to-metal contact area - the apparent overlap area barely matters. More or larger bolts, correctly torqued, raise force and lower resistance with diminishing returns as the constriction term shrinks. Torque beyond specification mostly yields the bolt rather than the joint; use a joint compound and correct surface preparation instead.
References
- Holm - Electric Contacts: Theory and Application, 4th ed., Springer 1967
- Slade - Electrical Contacts: Principles and Applications, 2nd ed., CRC Press