Bearing pressure

Bearing pressure is a particular case of contact mechanics often occurring in cases where a convex surface (male cylinder or sphere) contacts a concave surface (female cylinder or sphere: bore or hemispherical cup).

Excessive contact pressure can lead to a typical bearing failure such as a plastic deformation similar to peening.

Moreover, bearing pressure is restricted to the case where the charge can be described by a radial force pointing towards the center of the joint.

The complexity depends on the situation, and three cases are distinguished: By "negligible clearance", H7/g6 fit is typically meant.

If it is considered that the parts deform elastically, then the contact pressure is no longer uniform and transforms to a sinusoidal repartition:[6][7][8] with This is a particular case of the following section (θ0 = π/2).

In cases where the clearance can not be neglected, the contact between the male part is no longer the whole half-cylinder surface but is limited to a 2θ0 angle.

For a given system — given diameters and materials —, thus for given K and clearance j values, it is possible to obtain a curve θ0 = ƒ(F/(DL)).

The case is similar as above: when the parts are considered as rigid bodies and the clearance can be neglected, then the pressure is supposed to be uniform.

It can also be calculated considering the projected area:[3][10][11] As in the case of cylinder-cylinder contact, when the parts are modeled as elastic bodies with a negligible clearance, then the pressure can be modeled with a sinusoidal repartition:[6][12] with When the clearance can not be neglected, it is then necessary to know the value of the half contact angle θ0 , which can not be determined in a simple way and must be measured.

However, in all cases, the pressure that is calculated with the Hertz theory is greater than the actual pressure (because the contact surface of the model is smaller than the real contact surface), which affords designers with a safety margin for their design.

An equivalent module of elasticity is also defined: where νi is the Poisson's ratio of the material of the part i and Ei its Young's modulus.

[15] In plain bearings, the shaft is usually in contact with a bushing (sleeve or flanged) to reduce friction.

When the rotation is slow and the load is radial, the model of uniform pressure can be used (small deformations and clearance).

The product of the bearing pressure times the circumferential sliding speed, called load factor PV, is an estimation of the resistance capacity of the material against the frictional heating.

Bearing pressure for a cylinder-cylinder contact.
Uniform bearing pressure: case of rigid bodies when the clearing can be neglected.
Hemicylindrical body at the equilibrium in a fluid with hydrostatic pressure.
The elementary force d F , due to the pressure on a surface element d S , has two components: d F x and d F y .
Bearing pressure with a sinusoid repartition: case of elastic bodies when the clearing can be neglected.
Bearing pressure in case of elastic bodies when the clearance must be taken into account.
Elastic deformation in case of a male-female cylinders contact.
Bearing pressure in the case of a sphere-sphere contact.
Hertz contact stress in the case of a male cylinder-female cylinder contact.
Hertz contact stress in the case of a male sphere-female sphere contact.
Bearing pressure of a bolt on its passthrough hole. Case of two plates with a single overlap and one row of bolts.
Dimensions used to design a bolted connection according to the Eurocode 3 standard.