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{{continuum mechanics|cTopic=[[Solid mechanics]]}}

'''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: [[Boring (manufacturing)|bore]] or [[Spherical bearing|hemispherical cup]]). Excessive contact pressure can lead to a typical bearing failure such as a plastic deformation similar to [[peening]]. This problem is also referred to as '''bearing resistance'''.<ref name="Eurocode3">EN 1993-1-8:2005 ''[[Eurocode 3]]: Design of steel structures - Part 1-8: Design of joints''</ref>

== Hypotheses ==

A contact between a male part (convex) and a female part (concave) is considered when the radii of curvature are close to one another. There is no tightening and the joint slides with no friction therefore, the contact forces are [[Normal (geometry)|normal]] to the tangent of the contact surface.

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.

== Case of a cylinder-cylinder contact ==

[[File:Pression de contact cylindre cylindre.svg|thumb|400px|Bearing pressure for a cylinder-cylinder contact.]]

In the case of a [[revolute joint]] or of a [[hinge joint]], there is a contact between a male cylinder and a female cylinder. The complexity depends on the situation, and three cases are distinguished:
* the [[Engineering tolerance|clearance]] is negligible:
** a) the parts are [[rigid body|rigid bodies]],
** b) the parts are [[elastic body|elastic bodies]];
* c) the clearance cannot be ignored and the parts are elastic bodies.
By "negligible clearance", H7/g6 [[Engineering fit|fit]] is typically meant.

The axes of the cylinders are along the ''z''-axis, and two external forces apply to the male cylinder:
* a force <math>\vec{F}</math> along the ''y''-axis, the load;
* the action of the bore (contact pressure).
The main concern is the contact pressure with the bore, which is uniformly distributed along the ''z''-axis.

Notation:
* ''D'' is the nominal diameter of both male and female cylinders;<ref>due to the clearance, the diameter of the bore is bigger than the diameter of the male cylinder; however, we suppose that the diameters are close to each othert</ref>
* ''L'' the guiding length.

=== Negligible clearance and rigid bodies ===

[[File:Pression diametrale uniforme cylindre cylindre LF.svg|thumb|400px|Uniform bearing pressure: case of rigid bodies when the clearing can be neglected.]]

In this first modeling, the pressure is uniform. It is equal to<ref name="harvsp|SG|2003|p = 139">{{harvsp|SG|2003|p = 139}}</ref>{{,}}<ref>{{harvsp|GCM|2000|p = 177}}</ref>{{,}}:<ref>{{harvsp|Aublin|1992|pp = 108, 136}}</ref>
: <math>P = \frac{F}{D \times L} = \frac{\mathrm{radial\ load}}{\mathrm{projected\ area}}</math>.

{{clear}}

{{hidden information | title = Proof | info = There are two ways to obtain this result.

[[File:Pression objet hemicylindrique.svg|thumb|150px|Hemicylindrical body at the equilibrium in a fluid with hydrostatic pressure.]]

First, we can consider a hemicylinder in a fluid, with a uniform [[hydrostatic pressure]]. The equilibrium is achieved when the resulting force on the flat surface is equal to the resulting force on the curved one. The flat surface is a ''D'' × ''L'' rectangle, therefore
: ''F'' = ''P'' × (''D'' × ''L'')
q.e.d.

[[File:Force elementaire pression sur cylindre.svg|thumb|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''.]]

Second, we can integrate the pressure elementary forces. Consider a small surface dS on the cylindrical part, parallel to a generating line; its length is ''L'', and it is bound by the angles θ and θ + dθ. This small surface element can be considered as a flat rectangle which dimensions are ''L'' × (dθ × ''D''/2). The pressure force on the surface is equal to
: d''F'' = ''P'' × d''S'' = ½ × ''P'' × ''D'' × ''L'' × dθ
The (''y'', ''z'') plane is a plane of reflection symmetry, so the ''x'' compound of this force is annihilated by the force on the symmetrical surface element. The ''y'' compound of this force is equal to:
: d''F''''y'' = cos(θ) d''F'' = ½ × cos(θ) × ''P'' × ''D'' × ''L'' × dθ.
The resulting force is equal to
: <math>F_y = \int_{-\pi/2}^{\pi/2} \frac{1}{2} \times P \times D \times L\times \cos(\theta) \times \mathrm{d}\theta = \frac{1}{2} \times P \times D \times L \times \left [ \sin(\theta) \right ]_{-\pi/2}^{\pi/2} = P \times D \times L</math>
q.e.d.

This calculation is similar to the case of a [[Pressure vessel|cylindrical vessel under pressure]].
}}

=== Negligible clearance and elastic bodies ===

[[File:Pression diametrale variable sans jeu cylindre cylindre vue bout LF.svg|thumb|150px|Bearing pressure with a sinusoid repartition: case of elastic bodies when the clearing can be neglected.]]

If it is considered that the parts deform elastically, then the contact pressure is no longer uniform and transforms to a sinusoidal repartition<ref name="harvsp|SG|2003|p = 140">{{harvsp|SG|2003|p = 140}}</ref>{{,}}:<ref>{{harvsp|Aublin|1992|pp = 120–122, 136–137}}</ref>
: ''P''(θ) = ''P''max⋅cos θ
with
: <math>P_\mathrm{max} = \frac{4}{\pi} \cdot \frac{F}{L D}</math>.
This is a particular case of the following section (θ0 = π/2).

The maximum pressure is 4/π ≃ 1.27 times bigger than the case of uniform pressure.

{{clear}}

=== Clearance and elastic bodies ===

[[File:Pression diametrale variable avec jeu cylindre cylindre vue bout LF.svg|thumb|150px|Bearing pressure in case of elastic bodies when the clearance must be taken into account.]]

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. The pressure follows [[Hooke's law]]:<ref>{{harvsp|Aublin|1992|pp = 120–122, 137–138}}</ref>
: ''P''(θ) = ''K''⋅δα(θ)
where
* ''K'' is a positive real number that represents the rigidity of the materials;
* δ(θ) is the radial displacement of the contact point at the angle θ;
* α is a coefficient that represents the behaviour of the material:
** α = 1 for metals (purely [[elasticity (physics)|elastic behaviour]]),
** α > 1 for polymers ([[viscoelasticity|viscoelastic]] or [[viscoplasticity|viscoplastic]] behaviour).
The pressure varies as:
: ''A''⋅cos θ - ''B''
where ''A'' and ''B'' are positive real number. The maximum pressure is:
: <math>P_\mathrm{max} = \frac{4 F}{L D} \times \frac{1 - \cos \theta_0}{2\theta_0 - \sin 2\theta_0}</math>
the angle θ0 is in [[radian]]s.

The rigidity coefficient ''K'' and the half contact angle θ0 can not be derived from the theory. They must be measured. 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'')).

{{clear}}

{{hidden information | title = Proof | info = [[File:Action de contact ligne circulaire avec deformation contenant.svg|thumb|350px|Elastic deformation in case of a male-female cylinders contact.]]

'''Relationship between pressure, clearance and contact angle'''

The part no. 1 is the containing cylinder (female, concave), the part no. 2 is the contained cylinder (male, convex); the center of the cylinder ''i'' is ''O''''i'', and its radius is ''R''''i''.

The reference position is an ideal situation where both cylinders are concentric. The clearing, expressed as a radius (not diameter), is:
: ''j'' = ''R''1 - ''R''2.
Under the load, the part 2 gets in contact with the part 1, the he surfaces deform. we suppose that the cylinder 2 is rigid (no deformation), and that the cylinder 1 is an elastic body. The indentation of 2 into 1 has a depth of δmax; the cylinder movement is ''e'' (excentration):
: ''e'' = ''O''1''O''2 = ''j'' + δmax.

We considere the frame at the center of the cylinder 1 (''O''1, ''x'', ''y''). Let ''M'' be a point on the contact surface; θ is the angle (-''y'', ''O''1''M''). The displacement of the surface, δ, is:
: δ(θ) = ''O''1''M'' - ''R''1.
with δ(0) = δmax. The coordinates of ''M'' are:
: ''M''((''R''1 + δ(θ)⋅sin θ) ; -(''R''1 + δ(θ))⋅cos θ)
and the coordinates of ''O''2:
: ''O''2(0 ; -''e'').
Consider the frame (''O''1, ''u'', ''v''), where the axis ''u'' is (''O''1''M''). In this frame, the coordinates are:
: ''M''(''R''1 + δ(θ) ; 0)
: ''O''2(''e''⋅cos θ ; -''e''⋅sin θ)
We know that
: <math>\overrightarrow{O_1 M} = \overrightarrow{O_1 O_2} + \overrightarrow{O_2 M}</math>
thus
: <math>\left \{ \begin{align}
R_1 + \delta(\theta) & = & e \cdot \cos \theta + R_2 \cos \varphi \\
0 & = & -e \cdot \sin \theta + R_2 \sin \varphi
\end{align} \right .</math>
then we use the expression of ''e'' and ''R''1 = ''j'' + ''R''2:
: <math>\left \{ \begin{align}
j + R_2 + \delta(\theta) & = & (j + \delta_\max) \cdot \cos \theta + R_2 \cos \varphi \\
0 & = & -(j + \delta_\max) \cdot \sin \theta + R_2 \sin \varphi
\end{align} \right .</math>
The deformations are small, as we are in the elastic domain. Thus, δmax ≪ ''R''1 and therefore <nowiki>|</nowiki>φ<nowiki>|</nowiki> ≪ 1, i.e.
: cos φ ≃ 1
: sin φ ≃ φ (in [[radian]]s)
thus
: <math>\left \{ \begin{align}
(j + \delta_\max) \cdot \cos \theta + R_2 - (j + R_2 + \delta(\theta)) & = & 0\\
(j + \delta_\max) \cdot \sin \theta - R_2 \cdot \varphi & = & 0
\end{align} \right .</math>
and
: <math>\left \{ \begin{align}
(j + \delta_\max) \cdot \cos \theta - j - \delta(\theta) & = & 0\\
(j + \delta_\max) \cdot \sin \theta - R_2 \cdot \varphi & = & 0
\end{align} \right .</math>
At θ = θ0, δ(0) = 0 and the first equation is
: <math> (j + \delta_\max) \cdot \cos \theta_0 - j = 0
\Rightarrow \delta_\max = \frac{j(1 - \cos \theta_0)}{\cos \theta_0}
\Leftrightarrow \cos \theta_0 = \frac{j}{j + \delta_\max}</math>
and thus
: <math>\left ( j + \frac{j(1 - \cos \theta_0)}{\cos \theta_0} \right ) \cdot \cos \theta - j - \delta(\theta) = 0</math>
: <math>\Longrightarrow \delta(\theta) = j \left ( \frac{\cos \theta}{\cos \theta_0} - 1 \right )</math> '''[1]'''.
If we use the law of elasticity for a metal (α = 1):
:<math>\left \{ \begin{align}
P(\theta) & = & K \cdot j \left ( \frac{\cos \theta}{\cos \theta_0} - 1 \right ) \\
P_\max & = & K \cdot j \cdot \frac{1 - \cos \theta_0}{\cos \theta_0}
\end{align} \right .</math> '''[2]'''
The pressure is an [[affine function]] of cos θ:
: P(θ) = ''A''⋅cos θ - ''B''
with ''A'' = ''K''⋅''j''/cos θ0 and ''B'' = ''A''⋅cos θ0.

'''Case where the clearance can be neglected'''

If ''j'' ≃ 0 (R1 ≃ R2), then the contact is on the whole half-perimeter: 2θ0 ≃ π and cos θ0 ≃ 0. The value of 1/cos θ0 rise towards infinity, thus
: <math>\delta(\theta) \simeq j \frac{\cos \theta}{\cos \theta_0}</math>
As ''j'' and cos θ0 both tend towards 0, the ratio ''j''/cos θ0 is not defined when ''j'' goes to 0. In mechanical engineering, ''j'' = 0 is an uncertain fit, it is a nonsense, both mathematically and mechanically. We are looking for a limit function
: <math>P_{\pi/2}(\theta) = \lim_{\theta_0 \to \pi/2} P_{\theta_0}(\theta)</math>.

So, the pressure is a sinusoid function of θ:
: <math>P(\theta) = K \cdot \frac{j}{\cos \theta_0} \cdot \cos \theta</math>
thus
: ''P''(θ) = ''P''max⋅cos θ
with
: <math>P_\max = K \cdot \frac{j}{\cos \theta_0}</math>.
Consider an infinitesimal element of surface d''S'' bound by θ and θ + dθ. As in the case of the uniform pressure, we have
: d''F''''y''(θ) = cos(θ)d''F'' = ½ × cos(θ) × ''P''(θ) × ''D'' × ''L'' × dθ = ½ × cos2(θ) × ''P''max × ''D'' × ''L'' × dθ.
When we integrate between -π/2 and π/2, the result is:
: <math>F = \int_{-\pi/2}^{\pi/2} \mathrm{d}F_y (\theta) \mathrm{d}\theta
= \frac{1}{2}P_\max D L \int_{-\pi/2}^{\pi/2} \cos^2 \theta \mathrm{d} \theta</math>
We know that (e.g. using the [[Euler's formula]]):
: <math>\int_{-\pi/2}^{\pi/2} \cos^2 \theta \mathrm{d} \theta = \frac{1}{4} \left [ 2\theta + \sin 2\theta \right ]_{-\pi/2}^{\pi/2}
= \frac{1}{2} \left [ \theta + \sin \theta \cos \theta \right ]_{-\pi/2}^{\pi/2}
= \frac{\pi}{2}</math>
therefore
: <math>F = \frac{\pi}{4} P_\max D L</math>
and thus
: <math>P_\max = \frac{4}{\pi}\frac{F}{D L}</math>
q.e.d.

'''Case where the clearance can not be neglected'''

The force on an infinitesimal element of surface is:
: d''F''(θ) = ''P''(θ)d''S'' = ''K''δ(θ)d''S'' = ½ × ''K'' × ''j'' × cos θ/cos θ0 - 1) × d''S''
: <math>\mathrm{d}F_y = \frac{K j}{2} \left ( \frac{\cos \theta}{\cos \theta_0} - 1 \right ) D L \cos \theta \mathrm{d}\theta</math>
: <math>F = \frac{K j D L}{2} \int_{-\theta_0}^{\theta_0} \left ( \frac{\cos^2 \theta}{\cos \theta_0} - \cos \theta \right ) \mathrm{d} \theta
= \frac{K j D L}{2} \left [ \frac{\theta + \sin \theta \cos \theta}{2 \cos \theta_0} - \sin \theta \right ]_{-\theta_0}^{\theta_0}</math>
thus
: <math>F = \frac{K j D L}{2} \left ( \frac{2\theta_0 + 2 \sin \theta _0\cos \theta_0}{2 \cos \theta_0} - 2 \sin \theta_0 \right ) = \frac{K j D L}{2} \left ( \frac{\theta_0 - \sin \theta _0\cos \theta_0}{\cos \theta_0}\right )</math>.
We recognise the [[List of trigonometric identities#Double-angle formulae|trigonometric identity]] sin 2θ = 2 sin θ cos θ :
: <math>F = \frac{K j D L}{4 \cos \theta_0} ( 2\theta_0 - \sin 2\theta _0 )</math>
thus
: <math>K = \frac{4 F \cos \theta_0}{j D L( 2\theta_0 - \sin 2\theta _0 )}</math>
and therefore:
: <math>P_\max = K j \frac{1 - \cos \theta_0}{\cos \theta_0}
= \frac{4 F}{D L} \times \frac{1 - \cos \theta_0}{2\theta_0 - \sin 2\theta _0}</math>
q.e.d.
}}

== Case of a sphere-sphere contact ==

[[File:Pression de contact sphere sphere.svg|thumb|300px|Bearing pressure in the case of a sphere-sphere contact.]]

A sphere-sphere contact corresponds to a [[spherical joint]] (socket/ball), such as a ball jointed cylinder saddle. It can also describe the situation of [[bearing balls]].

=== Case of uniform pressure ===

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<ref name="harvsp|SG|2003|p = 139"/>{{,}}<ref>{{harvsp|GCM|2000|pp = 110–111}}</ref>{{,}}:<ref>{{harvsp|Aublin|1992|pp = 108, 144–145}}</ref>
: <math>P = \frac{F}{\pi R^2} = \frac{\mathrm{radial\ load}}{\mathrm{projected\ area}}</math>.

=== Case of a sinusoidal repartition of pressure ===

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<ref name="harvsp|SG|2003|p = 140"/>{{,}}:<ref>{{harvsp|Aublin|1992|pp = 120–122, 145–150}}</ref>
: ''P''(θ, φ) = ''P''max⋅cos θ
with
: <math>P = \frac{3}{2} \cdot \frac{F}{\pi R^2}</math>.

== Hertz contact stress ==

{{main article|Contact mechanics#Hertzian theory of non-adhesive elastic contact}}

[[File:Contact hertz cylindre male femelle.svg|thumb|400px|Hertz contact stress in the case of a male cylinder-female cylinder contact.]]

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. When this value is not available, the Hertz contact theory can be used.

The Hertz theory is normally only valid when the surfaces can not conform, or in other terms, can not fit each other by elastic deformation; one surface must be convex, the other one must be also convex plane. This is not the case here, as the outer cylinder is concave, so the results must be considered with great care. The approximation is only valid when the inner radius of the container ''R''1 is far greater than the outer radius of the content ''R''2, in which case the surface container is then seen as flat by the content. 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.

In this theory, the radius of the female part (concave) is negative.<ref>{{harvsp|Fanchon|2001|pp = 467–471}}</ref>

A relative diameter of curvature is defined:
: <math>\frac{1}{d^*} = \frac{1}{d_1} + \frac{1}{d_2}</math>
where ''d''1 is the diameter of the female part (negative) and ''d''2 is the diameter of the male part (positive). An equivalent module of elasticity is also defined:
: <math>\frac{1}{E^*} = \frac{1 - \nu^2_1}{E_1} + \frac{1 - \nu^2_2}{E_2}</math>
where ν''i'' is the [[Poisson's ratio]] of the material of the part ''i'' and ''Ei'' its [[Young's modulus]].

For a cylinder-cylinder contact, the width of the contact surface is:
: <math>b = \left ( \frac{2 F}{\pi L} \cdot \frac{d^*}{E^*} \right )^{1/2}</math>
and the maximal pressure is in the middle:
: <math>P_\max = \frac{2 F}{\pi b L} = \sqrt{\frac{2 F E^*}{\pi L d^*}}</math>.

[[File:Contact hertz sphere male femelle.svg|thumb|400px|Hertz contact stress in the case of a male sphere-female sphere contact.]]

In case of a sphere-sphere contact, the contact surface is a disk whose radius is:
: <math>a = \left ( \frac{3 F}{8} \cdot \frac{d^*}{E^*} \right )^{1/3}</math>
and the maximal pressure is in the middle:
: <math>P_\max = \frac{3 F}{\pi a^2} = \frac{4}{\pi} \sqrt[3]{3 F \left ( \frac{E^*}{d^*} \right )^2}</math>.

== Applications ==

=== Bolt used as a stop ===

[[File:Pression diametrale assemblage boulonne 2 plaques 1 rangee vis.svg|thumb|400px|Bearing pressure of a bolt on its passthrough hole. Case of two plates with a single overlap and one row of bolts.]]

[[File:Notation cotes rangees boulons pression diametrale eurocode 3.svg|thumb|400px|Dimensions used to design a bolted connection according to the Eurocode 3 standard.]]

In a bolted connection, the role of the [[Bolt (fastener)|bolts]] is normally to press one parts on the other; the [[Adhesion|adherence]] ([[friction]]) is opposed to the tangent forces and prevents the parts from sliding apart. In some cases however, the adherence is not sufficient. The bolts then play the role of stops: the screws endure [[shear stress]] whereas the hole endure bearing pressure.

In good design practice, the threaded part of the screw should be small and only the smooth part should be in contact with the plates; in the case of a [[shoulder screw]], the clearance between the screw and the hole is very small ( a case of rigid bodies with negligible clearance). If the acceptable pressure limit ''P''lim of the material is known, the thickness ''t'' of the part and the diameter ''d'' of the screw, then the maximum acceptable tangent force for one bolt ''F''b, Rd (design bearing resistance per bolt) is:
: ''F''b, Rd = ''P''lim × ''d'' × ''t''.
In this case, the acceptable pressure limit is calculated from the ultimate tensile stress ''f''u and factors of safety, according to the [[Eurocode 3]] standard<ref name="Eurocode3" />{{,}}.<ref name="Seinturier">{{cite book
| first1 = Francine
| last1 = Seinturier
| language = fr
| title = Construction métallique 2
| chapter = C-viii Assemblages boulonnés
| publisher = IUT Grenoble I
| url = http://iut-tice.ujf-grenoble.fr/tice-espaces/GC/cm2/chap08/boulons1.pdf
| access-date = 2015-12-04
| archive-url = https://web.archive.org/web/20111125050842/http://iut-tice.ujf-grenoble.fr/tice-espaces/GC/cm2/chap08/boulons1.pdf
| archive-date = 2011-11-25
| url-status = dead
}}</ref> In the case of two plates with a single overlap and one row of bolts, the formula is:
: ''P''lim = 1.5 × ''f''u/γM2
where
* γM2 = 1.25: partial safety factor.
In more complex situations, the formula is:
: ''P''lim = ''k''1 × α × ''f''u/γM2
where
* ''k''1 and α are factors that take into account other failure modes than the bearing pressure overload; ''k''1 take into account the effects that are perpendicular to the tangent force, and α the effects along the force;
* ''k''1 = min{2.8''e''2/''d''0 ; 2.5} for end bolts, ''k''1 = min{1.4''p''2/''d''0 ; 2.5} for inner bolts,
** ''e''2: edge distance from the centre of a fastener hole to the adjacent edge of the part, measured at right angles to the direction of load transfer,
** ''p''2: spacing measured perpendicular to the load transfer direction between adjacent lines of
fasteners,
** ''d''0: diameter of the passthrough hole;
* α = min{''e''1/3''d''0 ; ''p''1/3''d''0 - 1/4 ; ''f''ub/''f''u ; 1}, with
** ''e''1: end distance from the center of a fastener hole to the adjacent end of the part, measured in the direction of load transfer,
** ''p''1: spacing between centers of fasteners in the direction of load transfer,
** ''f''ub: specified ultimate tensile strength of the bolt.

{| class="wikitable"
|+ Ultimate tensile stress for usual structural steels<ref name="Eurocode3" />{{,}}<ref name="Seinturier" />
|-
! scope = "row" | Steel grades (EN standard)
| S235 || S275 || S355
|-
! scope = "row" | Ultimate tensile stress ''f''u (MPa)
| 360 || 430 || 510
|}

When the parts are in wood, the acceptable limit pressure is about 4 to 8.5 MP.<ref>{{cite web
| url = http://www.gramme.be/unite9/pmwikiOLD/pmwiki.php?n=PrGC0607.Assemblages
| title = Assemblages
| language = fr
| website = Wiki de l'Unité Construction de Gramme
| author = MB
| date = April 2007
| access-date = 2015-11-25
}}</ref>

=== Plain bearing ===

In [[plain bearing]]s, the [[Shaft (Mechanical Engineering)|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<ref>{{harvsp|Fanchon|2011|p = 255}}</ref>{{,}}<ref>{{harvsp|Chevalier|2004|p = 258}}</ref>{{,}}.<ref>{{harvsp|GCM|2000|pp = 113–116, 176–181}}</ref>

{| class="wikitable"
|+ Acceptable bearing pressure<ref>{{cite book
| language = fr
| chapter = Paliers lisses ou coussinets
| title = Construction mécanique
| publisher = Université de Toulon
| author = L.P. Pierre et Marie Curie, Aulnoye
| url = https://moodle.univ-tln.fr/pluginfile.php/50684/mod_resource/content/1/Les-Paliers-lisses-ou-Coussinets.pdf
| format = PDF
}}</ref>
|-
! scope="col" | Type of bushing Maximal circumferential sliding speed
! scope="col" | Acceptable bearing pressure (MPa)
|-
| Self-lubricating bushels 7 to 8 m/s 13 m/s for graphite
| graphite: 5 lead bronze: 20 to 30 tin bronze: 7 to 35
|-
| Composite bushing, Glacier 2 to 3 m/s
| acetal: 70 PTFE: 50
|-
| Polymer bushing 2 to 3 m/s || 7 to 10
|}

== References ==
{{reflist|2}}

== Bibliography ==

* [Aublin 1992] {{cite book
| ref=CITEREFAublin1992
| language = fr
| first1 = Michel | last1 = Aublin
| first2 = René | last2 = Boncompain
| first3 = Michel | last3 = Boulaton
| first4 = Daniel | last4 = Caron
| first5 = Émile | last5 = Jeay
| first6 = Bernard | last6 = Lacage
| first7 = Jacky | last7 = Réa
| title =Systèmes mécaniques : théorie et dimensionnement
| publisher = [[Dunod]]
| date = 1992
| isbn = 2-10-001051-4
| pages = 108–157
}}
* [Chevalier 2004] {{cite book
| ref=harv
| language = fr
| first1 = André | last1 = Chevalier
| title = Guide du dessinateur industriel
| publisher = [[Hachette (publisher)|Hachette technique]]
| date = 2004
| isbn = 978-2-01-168831-6
| pages = 258
}}
* [Fanchon 2001] {{cite book
| ref=harv
| language = fr
| first1 = Jean-Louis | last1 = Fanchon
| title = Guide de mécanique : sciences et technologies industrielles
| publisher = [[Éditions Nathan|Nathan]]
| pages = 467–471
| date = 2001
| isbn = 978-2-09-178965-1
}}
* [Fanchon 2011] {{cite book
| ref=harv
| language = fr
| first1 = Jean-Louis | last1 = Fanchon
| title = Guide des sciences et technologies industrielles
| publisher = [[Afnor]]/[[Éditions Nathan|Nathan]]
| chapter = Calcul des coussinets (régime non hydrodynamique)
| pages = 255–256
| date = 2011
| isbn = 978-2-09-161590-5
}}
* [GCM 2000] {{cite book
| language = fr
| ref=CITEREFGCM2000
| first1 = C. | last1 = Texeido
| first2 = J.-C. | last2 = Jouanne
| first3 = B. | last3 = Bauwe
| first4 = P. | last4 = Chambraud
| first5 = G. | last5 = Ignatio
| first6 = C. | last6 = Guérin
| title = Guide de construction mécanique
| publisher = [[Éditions Delagrave|Delagrave]]
| pages = 110–116, 176–180
| date = 2000
| isbn = 978-2-206-08224-0
}}
*[SG 2003] {{cite book
| language = fr
| ref=CITEREFSG2003
| first1 = D. | last1 = Spenlé
| first2 = R. | last2 = Gourhant
| title = Guide du calcul en mécanique : maîtriser la performance des systèmes industriels
| publisher = [[Hachette (publisher)|Hachette technique]]
| date = 2003
| isbn = 2-01-16-8835-3
| pages = 139–140
}}

[[Category:Bearings (mechanical)]]
[[Category:Mechanical engineering]]
[[Category:Solid mechanics]]

Bearing pressure - Revision history

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