Coefficient of Friction

Definition and Basic Equations

The coefficient of friction (symbol μ) describes how strongly two bodies “brake” against each other at their contact face when they are to be moved against each other, or are already moving. It is a dimensionless parameter, because it is defined as the ratio of two forces, and the units cancel out.

The underlying definition is:

$$\mu =\frac{F_R}{F_N}$$

Here, $F_R$ is the friction force (acting parallel to the contact face) and $F_N$ is the normal force (acting perpendicular to the contact face). In many technical calculations, an approximation is used:

$$F_R\approx \mu \cdot F_N$$

This relationship is a model. In real sealing contacts, it frequently deviates, because lubrication, surface condition, and operating state co-determine the friction value.

A clear distinction helps for classification: μ is not a force but a ratio. The friction force $F_R$ is the actual force that acts against motion. The break-away force denotes the force value needed to start the transition from standstill to motion.

Static and Sliding Friction (μ_H, μ_G)

When two contact partners initially stand still, this is called static friction. The friction force can rise with the applied tangential force until a maximum is reached. This maximum corresponds practically to the break-away force. The associated parameter is the static friction coefficient ${\mu }_H$.

As soon as motion sets in, sliding friction usually applies. Then the friction force frequently settles at a lower, more stable level. The associated parameter is the sliding friction coefficient ${\mu }_G$. In many applications, ${\mu }_H>{\mu }_G$ applies, which is why break-away frequently requires more drive force than uniform sliding.

Why μ Is Not Constant in Practice (Tribology, Stribeck)

In practice, μ is rarely a fixed material constant. The reason lies in tribology — that is, the science of friction, wear, and lubrication. Friction arises not only from “material against material”, but from a contact that is shaped by lubricating film, surface roughness, temperature, contact pressure, and motion state.

For seals, this is particularly important, because pure dry friction is rarely present here. Instead, boundary or mixed friction is frequently found. This means: part of the load is transferred via solid-body contacts, part via a lubricating film. As a result, μ strongly depends on viscosity (the viscosity of the lubricant), speed, surface pressure, and temperature.

This dependence is often described with the Stribeck curve. It shows how μ changes over speed (and the associated lubricating-film conditions): at very low speeds, μ is frequently higher, then drops in the transition to better lubrication, and can reach another level under pronounced fluid friction.

Friction Regimes in Sealing Contacts

The following terms describe how the contact partners are separated and why μ changes:

• Boundary friction: Lubricant is present, but the surfaces still touch directly frequently. μ is often relatively high here and strongly state-dependent.

• Mixed friction: Part of the load runs via direct contact, part via a lubricating film. μ is frequently lower than in boundary friction but can be unstable.

• Hydrodynamic friction: A load-bearing fluid film largely separates the surfaces. Friction then arises mainly from shear in the fluid.

Sealing contacts in many hydraulic and pneumatic applications lie predominantly in the boundary to mixed friction range — particularly with small strokes, low speeds, or frequent start-stop operation.

Coefficient of Friction in Seals: Break-Away Force, Stick-Slip, and Effects

In sealing technology, μ is particularly critical when motion must be precise or when jerking is to be avoided. A typical effect is stick-slip. Here, sticking and sliding alternate repeatedly. The cause is frequently that static friction is noticeably higher than sliding friction and that the friction coefficient initially drops as speed rises. Then a higher friction force builds up during standstill, motion starts jerkily, and friction subsequently drops again.

The consequences appear directly in system behavior: positioning errors, vibrations, and noise arise. In addition, the requirement on drive design rises, because the force required to break away and the force during steady running can lie apart.

In practice, μ and the break-away force are influenced via a few central control variables that act together: material pairing (e.g., elastomer/metal), lubrication, surface quality, and seal geometry. The goal is usually uniform friction across the relevant operating range and a small jump between ${\mu }_H$ and ${\mu }_G$.

Measurement, Comparability, and Typical Specification of μ

A coefficient of friction is only meaningfully comparable when the test conditions are clearly defined. For μ depends on which load is applied, how fast motion is, which counter body is used, and which climate (temperature, humidity) prevails. Therefore, many test approaches also explicitly distinguish between start-up friction value (close to ${\mu }_H$) and sliding friction value (close to ${\mu }_G$).

For plastics and polymer-based sealing materials, established standards-oriented test methods exist that define precisely such operating conditions. In sealing technology, however, it is important to document μ as a result of material pairing, surface, lubrication, and operating state. A statement such as “μ = 0.1” is hardly reliable from a technical point of view without these conditions.

For complex sealing tasks, specialized tribological consultation can be sensible to reliably assess μ under real operating conditions.