8/2/2019 Friction 1

1/22

Friction

8/2/2019 Friction 1

2/22

Types of friction and Laws

Friction: Resistance to motion when one solid body slides over the

other.Direction of Friction force opposite to motion

Static friction: Friction force required to start sliding

Kinetic friction: Friction force required to maintain sliding

Kinetic friction < Static friction

Laws of Friction: (Totally empirical & obeyed most of the times)

Amontons laws:

Friction is independent of apparent area of contact of the twobodies. (Valid for materials having definite yield point)

Force of friction is proportional to the Normal load. (valid only underlower pressures)

Coulombs law:

Kinetic friction is independent of the speed of sliding.

8/2/2019 Friction 1

3/22

Coefficient of Friction

W

F

WF

WF

W

F

W

F

k

k

s

s

Coefficient of friction can be static or kinetic or rolling coefficient of friction.

Coefficient of friction is for a combination of two materials under a given set of

surface.r for steel roller on a steel surface is 0.001.

Factors important for friction:

Shape and contour of the surface.

The way surfaces deform when pressed.

Adhesion of solids

Strength properties at the interface

Surface films and their role

Mechanism of energy loss under deformation

W

Fr

r

8/2/2019 Friction 1

4/22

Basis of Amontons Laws

Begin with following assumptions,

1) During sliding, frictional force per unit area (s) is constant,Frictional force, F = A s

A is real area of contact

2) Real area of contact (A) is proportional to the normal load W.

A = q W; q is constant of proportionality

Therefore,

3) F = q W s

If assumptions are justified,

equation 1 & 2, state thatFriction force depends upon the real area of contact.

Friction force is independent of the apparent area of contact.

equation 3, state that

Friction force is proportional to normal load.

8/2/2019 Friction 1

5/22

8/2/2019 Friction 1

6/22

Measurement of Friction

Prediction of coefficients of friction is not possible.

Pauli: God made solids, but surfaces are made by Devil.

Best way is to measure the friction.Basic Methodology:

To place two specimens together under a known normal load.

Slide one specimen w.r.t. the other

Measure the tangential force resisting sliding.

Most common method: Inclined plane test. (static friction)

S S cos

S sin

tancos

sin

S

S

W

F

At the point of sliding,

8/2/2019 Friction 1

7/22

For continuous sliding friction,

Force is measured by a dynamometer.

Various configurations are used.

Conforming / non conforming Flat Pin on disc

Pin stationary, disc rotating

Multiple pass /single pass

Speed of disc drive continuously

changed Pin on Cylinder

Crossed cylinders

Reciprocating Rig

All measurements should be carriedout in enclosed environment.

8/2/2019 Friction 1

8/22

Origins of Friction

Interactions between asperities

Each asperity interaction contributes to friction Total friction is summation of friction at individual contacts

Energy dissipated is summation of energy dissipated at individualcontacts

At any time friction force is almost constant. Why?

Statistical distribution of contact process is almost constant.

Under equilibrium, energy dissipated = F . U [U velocity]

Friction can be explained by two approaches:

By the origins of forces.By the process of energy dissipation (Adhesion or deformation)

8/2/2019 Friction 1

9/22

Theories of Friction

1. Simple Adhesion Theory: [Bowden & Tabor (1950)]

1. Under load conditions, surfaces make contact only at the tips of

asperities.2. Even at low loads, real contact pressures are very high and the

asperity tips of softer material have plastic deformation

3. The plastic deformation results in increase of the total contact area(growth of individual initial contacts + formation of new contacts), untilthe real area of contact is just sufficient to support the load elastically.

4. Thus, W = A poA Actual / real contact area

po yield pressure (stress) of the softer material

As po H H hardness in indentation test

W = A. H5. Due to severe plastic deformation, cold welding takes place at theasperity contacts i.e. strong adhesive bonds are formed.

6. Friction force, F = A. s and = F/W = s/H

s specific friction force (force required to cause shear failure of unitarea of asperity junction)

8/2/2019 Friction 1

10/22

Simple Adhesion Theory

Provided first theoretical explanation of Amontons laws.

(Friction Independent of apparent area and proportional to normal load)

Now, if s = k (critical stress)

= k / H.

k/H is almost constant for most materials.

i.e. many material pairs have similar value of (0.16)

Effect of ploughing (hard asperity making a groove in softer material) isincluded by adding ploughing to k / H.

Softer material

Hard asperity

8/2/2019 Friction 1

11/22

Limitations of Simple Adhesion Theory

= k / H, indicates that only depends on properties of softer

material. This means, a material should have same with any other harder

material. This is not seen.

Normal values of for metal pairs are 0.5 and not 0.16.

For many ductile materials,

much higher (>1 also) when surfaces are free of any contaminant.No sliding takes place.

Cold welding almost for much of the nominal contact area.

Theory needs modification

8/2/2019 Friction 1

12/22

Extension of the Simple Theory of Adhesion

Junction Growth:

Consider a 2D stress system,

Assumption: Yielding takes place atmax = k

k is radius of the Mohrs circle,

222)

2

( kp

p

k

Normal stress

Shear stress

22244 kp

For a single asperity junction,

Area of contact A = W/H

= max = k

Any increase in Normal stress or shearstress will cause plastic flow.

Any increase in tangential force (F)leads to increase in contact area, calledas Junction Growth

Normal & shear stress decrease asarea increases, till max = k, when load issupported elastically.

F increases further, again junctiongrowth.

Normal force remains same, but Fcontinues to rise

Ratio / attains very high value.

(Limited by strength of softer material)

8/2/2019 Friction 1

13/22

Even after removing normal load, strong resistance to shear is observed.

For a 3 D contact, it is assumed that,

p2 + 2 = r2 { & r are constants, obtained from boundary conditions}

1) When tangential force = 0, = 0 and p = Hr2 = H2 and p2 + 2 = H2

2) After junction growth, >> p

2 = H2 as k = H2 / k2

9 according to Bowden < 9 (Actual)

What is important ?

For large scale junction growth, >> p.

As max is limited by shear strength of the softer material,

Means, p

8/2/2019 Friction 1

14/22

Why is low under normal conditions

1. Junctions formed are weaker in shear than those formed in cleansurfaces.

2. Weakness is due to formation of film.

If, s = c k where, s = shear strength of film, c = constant < 1.

When, frictional stress, F/A < s , junction growth continues.

When, F/A = s , film shearing takes place and sliding occurs.

Condition for sliding:p2 + s

2 = H2 But, H2 = k 2

Therefore, p2 + s2 = k 2

p2 + s2 = s

2 / c2

2/12)]1([ c

cps

As c 1, infinity

When c is small, = c /0.5, Principle of lubricationby using soft metal films & bounary lubricants

8/2/2019 Friction 1

15/22

Variation of against c for different values of .

Except at large value of c, value of is not of much importance

8/2/2019 Friction 1

16/22

Modifications by Johnson and Halling

2/12

12)][ c

c

Johnson proposed,

If, 2 - 1 >1, 1 even if c =1.

As c 1, sliding causes 1.

It is then possible to produce, > 1, not by further junction growth but byinternal shear in the junction.

This can be, by forming a chip or prow with adhesive transfer tothe opposing surface.

Halling suggested that is not constant and it is a function of c.

= [2/(1-a1)]2 and = ck/ p = c / [ (1 - c2) ]1/2

= 36 when c = 0 and infinity when c 1

Important Outcome: Friction coefficient depend on -

1. Interfacial shear strength.

2. Deformation characteristics of the material

8/2/2019 Friction 1

17/22

Effect of ploughing:

Softer material

Hard conical

asperity

Wi

r

During rubbing, only the front surfaceis in contact with the softer surface.

Wi is supported by horizontalprojection of asperity contact.

Wi = r2 H

Frictional force Fi, is supported byvertical projection

Fi = r h H

Hence, = Fi / Wi = 2 h / r

= [2 cot ] /

For most surfaces ploughing component of friction is very small.

h

8/2/2019 Friction 1

18/22

Theories of Friction

2. Deformation Theories:

First proposed by Green (1955) Later extended by Edward and Halling (1968).

Takes into account the fact that and on the asperities vary with life ofjunction.

Physical basis of deformation theory:

In sliding of microscopically flat surface,

Motion is parallel to the interface.

Separation of the surfaces remain constant.

This must be so,

To maintain the area of contact at constant level to support constant normal load

Main outcome,Contacting asperities must deform to allow movement to continue.

8/2/2019 Friction 1

19/22

])1(

1[

])1(

[

2/12

2/12

c

cc

c

function of c and geometry of the junction

= 0, when = 0. ( = semi angle of asperity)

= constant H2/ k2

c is constant < 1

What happens when = 0?

8/2/2019 Friction 1

20/22

Variation of Normal force and Friction Force throughout ajunction life, for junction angle 100.

8/2/2019 Friction 1

21/22

Variation of against c for various junction angles

8/2/2019 Friction 1

22/22

Energy consumed in plastic deformation increases with thesharpness of asperities.

For elastic deformation of asperities,

Deformation component of friction is zero. Real area of contact and force for shearing increase with slope of

asperity.

Hence, friction between microscopically smooth surfaces increasewith the mean absolute surface slope.

Interaction of Adhesion and Deformation:

1. Adhesion and deformation theories are not competitive butcomplementary

2. Any time, friction will have adhesion + deformation contributions

3. These components of friction are not additive, but interactive.