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Static and kinetic friction coefficient
m=F/W
W Normal load
Tangential force
P
Friction force F
Time
Fric
tio
n f
orc
e
( ) ( )
Static friction coefficient : Fs/W at slip initiation Kinetic friction coefficient : Fs/W at during sliding
Amonton-Coulomb Law for sliding friction
(1) Friction force is proportional to normal load.
(2) Friction force is independent of apparent contact area.
(3) Friction force is independent of sliding velocity.
(4) Static friction force is larger than kinetic friction force.
F
2F
F Fr
icti
on
forc
e Static friction force
kinetic friction force
Sliding velocity
Normal load, N
Fric
tio
n c
oef
fici
ent
Fric
tio
n c
oef
fici
ent
Apparent contact area, mm2
Wood/steel Dry condition Normal load: 0.3 N
Friction coefficient is independent of normal load, sliding velocity, and contact area.
(3.1)
Amonton-Coulomb Law for sliding friction
Fric
tio
n c
oef
fici
ent
Fric
tio
n c
oef
fici
ent
Sliding velocity, mm/s Contact time, s
Steel/Indium
Steel/Lead
Steel/steel Dry sliding
Amonton-Coulomb Law for sliding friction
There are lots of cases where the Amonton-Coulomb friction law is not established.
F = Fa + Fp (Fh)
Adhesion at real contact area
Ploughing due to penetration by hard
asperities
strain
Stress
Hysteresis energy loss
Elastic hysteresis loss
Friction mechanism
(3.2)
Adhesion friction theory
Friction force
橋本巨著，基礎から学ぶトライボロジー，森北出版（株），(2006)
Normal load Traction force
Friction force：Force to shear adhesion in the real contact area
ro
n
i
n
i
rioi AsAsFF
1 1
so: maximum shear strength Ar：real contact area W: normal load p0: plastic flow pressure
0p
s
W
As
W
F oro m
(3.3)
(3.4)
Hard ball Hard ball Hard ball
Hard Hard Soft
Soft film
Asmall Alarge Amedium
slarge ssmall ssmall
Effect of soft film on hard substrate
>
Modified Adhesion friction theory W
A0 = Wp0
FT
W
A > Wp0
More significant plastic flow occurs when the tangential force is applied. → Junction Growth
222
0 spp
Condition for plastic deformation when the normal pressure and shear pressure are applied.
22
2
0
A
F
A
Wp T
A
(3.5)
(3.6)
(3.7)
Effect of surface roughness on friction coefficient W
P F
32
W
P F
Rough Smooth Fr
icti
on
co
effi
cie
nt
F : 摩擦力 r : 材料表面における突起半径 W : 垂直荷重 h : 食込み深さ A : 投影面積 m : 摩擦係数 p0 : 塑性流動圧力 V : 垂直方向 n : 突起総数 2q : 突起の角度 H : 進行方向
q
r
h
F
W Conical asperity
r
q
r
AH h
A conical asperity is penetrated into the surface and moves in the right direction
2
2rnAv
Av
q
m
cotr
h
W
F
nrhppAF
pr
nAvpW
H
22
2
00
0
2
0
nrhAH
Ploughing friction
Soft
Hard
(3.8)
(3.9)
(3.10)
Hysteresis friction
strain
Stre
ss
Hysteresis energy loss F
W
Viscoelastic material
Hard asperity
Loading unloading
s
S-S curve for viscoelastic materials under compression
( ) > ( )
Hysteresis friction is caused by the energy dissipation due to cyclic deformation (loading and unloading) for viscoelastic materials such as rubbers.
Method to reduce friction and wear
Hydrodynamic lubrication
Hydrostatic lubrication
Solid lubricants (powder form)
Solid lubricating film Self lubricating materials
Rolling type guide Magnetic force
Boundary lubrication by adsorbed molecular films
How to reduce adhesion in the contact area is key to reduce friction.
Stick slip phenomena
Slip
Stick
Fric
tio
n f
orc
e F
, N
Time t, s
Fs
Fk
F
v
x k
m
Mechanical mode of friction vibration Friction force as a function of time when stick-slip occurs
0 kxxm)v(xm m (3.11)
0
0
dv
d)v(
dv
d)v(
mm
mm
( )
( )
Characteristics
Practical applications of RB ceramics
RB ceramics
Carriage
Guide rail
RB ceramics
Carriage
Guide rail
Guide rail：Stainless steel
Slider：RB ceramics
Guide rail：Stainless steel
Slider：RB ceramics
Dry-type linear sliding bearings using RB ceramics
A dry-type linear sliding bearing using RB ceramics was developed collaborated with Japanese company
and has been in practical use since 2001.
Overview Structure
Oil free Maintenance free Noise free Capability to be used at high velocity over 1m/s Capability to be used in water
Pamphlet of newly developed dry linear sliding bearing
Type of Bearings
Dry linear sliding bearing
using RB ceramics
Grease-lubricated linear
rolling bearing
Sliding velocity 680mm/s 500mm/s
Maximum noise level 40.5dB 69.4dB
Sound pressure ratio 3% 100%
Noise level data
RB ceramics
Carriage
Guide rail
RB ceramics
Carriage
Guide rail
Guide rail：Stainless steel
Slider：RB ceramics
Guide rail：Stainless steel
Slider：RB ceramics
RBセラミックスガイドの静粛性 Quietness Suppression of stick-slip motion by using RB ceramics
