# How Can You Calculate Force to Overcome Friction From an O-Ring Seal?

I essentially have a piston in a tube that is sealed with an O-Ring and actuated with a solenoid.

The friction of the O-Ring however, is higher than estimated (guessed as far as I can tell) by the designer who doesn't have any calculations to show me as reference. I have searched a little with no luck. The piston is pushed back to it's original position (after the solenoid is deactivated) by a spring, but the 5 Newton force the spring provides is not enough to overcome the friction of the seal.

To get an idea of the force required I attached a bolt and added weight until the piston moved, but theoretically, is there a simple way of calculating the force required to overcome the friction of a rubber O-Ring seal?

A paper or two exists with relatively complex mathematical models, which i don't have the time to reproduce. Given how common rubber O-Rings are I'd be surprised if there weren't a commonly used formula.

• Common rubber and rubberlikes have suprisongly wide range of properties Apr 11, 2018 at 17:27
• The limiting factor in problems like this is usually 'sticktion', or the force required to start moving from a standstill, rather than the force to keep sliding after movement has started. It's notoriously difficult to estimate, can vary wildly with just a few % change in compression, or minor variations in seal geometry. Adding some lubricant to the seal or replacing it with a PTFE coated equivalent may offer a quick fix. Jan 3, 2021 at 12:58
• Unfortunately I don't think you will be able to reliably calculate this force. There are too many small factors like the state of lubrication, surface finish of the parts, hardening of the o-ring over time. Swelling due to liquid absorption. Thermal expansion, and softening, etc. I could probably go on forever.
– Drew
Jun 3, 2021 at 6:06

The friction is depended from the normal force and the friction coefficient. The friction coefficient is an empirical property of the contacting materials.

The normal force is depended of the impression of the O-ring. Normally your designer will use the prescribed dimensions given by the O-ring manufacture.

You have measured the F force. Therefore you can modify the Normale force (impressing of the O-ring) by less impression OR/AND change the 𝛄 friction coefficient. On wikipedia you will find reference values for different material.

We know that friction formulas only depend on the coefficient of friction and the normal force. It does not depend the area of contact; it doesn't depend on the sliding speed.

So, the crux of this is 1. what is the material and the coeff. of the material. And 2. what is the normal force? Point 2 I think is what your asking? Am I right?

i) get the uncompressed diameter of the o-ring. ii) based on the (worst case) inner and outer diameter of the surfaces the o-ring rests between, what is the compressed diameter? iii) express this as a percentage. iv) you should be able to compare this to the contact force versus normal force / mm graph for the o-ring. It will look a bit like y=x2, with min, max & norm lines.

With any luck you should arrive at an answer that explains what you are seeing, taking into account the tolerances.

N.B This assume that o-ring is free to distort out between the inner and outer surfaces. If it's really tight in there, all bets are off.