Engineering Mechanics: Statics Chapter 8: Friction Chapter 8: Friction.

Engineering Mechanics: StaticsEngineering Mechanics: Statics

Chapter 8: Friction

Chapter 8: Friction

Chapter ObjectivesChapter Objectives

To introduce the concept of dry friction and show how to analyze the equilibrium of rigid bodies subjected to this force.

To present specific applications of frictional force analysis on wedges, screws, belts, and bearings.

To investigate the concept of rolling resistance.

Chapter OutlineChapter Outline

Characteristics of Dry FrictionProblems Involving Dry FrictionWedgesFrictional Forces on ScrewsFrictional Forces on Flat BeltsFrictional Forces on Collar Bearings,

Pivot Bearings, and DisksFrictional Forces on Journal BearingsRolling Friction

8.1 Characteristics of Dry Friction


Friction or retards slipping of the body relative to a

second body or surface which it is in contact Acts tangent to the surfaces at points of

contact with other body Opposing possible or existing motion of the

body relative to points of contact Two types of friction – Fluid and Coulomb

Friction



Fluid friction exist when the contacting surface are separated by a film of fluid (gas or liquid)

Depends on velocity of the fluid and its ability to resist shear force

Coulomb friction, also known as dry friction, occurs between contacting surfaces of bodies in the absence of a lubricating fluid



Theory of Dry Friction Consider the effects caused by pulling

horizontally on a block of uniform weight W which is resting on a rough horizontal surface

Consider the surfaces of contact to be nonrigid or deformable and other parts of the block to be rigid



Theory of Dry Friction FBD of the block The floor exerts a distribution of

the normal force ∆Nn and frictional force ∆Fn along the contact surface

For equilibrium, the normal forces act upward to balance the block’s weight W, and the frictional forces act to the left to prevent force P from moving the block to the right



Theory of Dry Friction Examining the contacting surfaces

between the floor and the block, it can seen that many microscopic irregularities exist between the two surfaces

Reactive forces ∆Rn developed at each of the protuberances



Theory of Dry FrictionThese forces act at all points of

contact and each reactive force consist of both a frictional component ∆Fn and a normal component ∆Nn



Theory of Dry FrictionEquilibrium Effect of normal and frictional

loadings are indicated by their resultant N and F

Distribution of ∆Fn indicates that F is tangent to the contacting surface, opposite to the direction of P

Normal force N is determined from the distribution of ∆Nn



Theory of Dry Friction N is directed upward to

balance W N acts a distance x to the

right of the line of action of W This location coincides with

the centroid or the geometric center of the loading diagram in order to balance the “tipping effect” caused by P



Theory of Dry FrictionExample P is applied at a height h from the

surface Moment equilibrium about point O

is satisfied if W x = Ph or x = Ph/W

The block is on the verge on tipping if N acts at the right corner of the block, x = a/2



Theory of Dry FrictionImpending Motion In cases where h is small or surfaces of

contact are rather “slippery”, the frictional force F may not be great enough to balance P and consequently, the block will tend to slip before it can tip

As P is slowly increased, F correspondingly increase until it attains a certain maximum value F, called the limiting static frictional force



Theory of Dry Friction When this value is reached, any further

increase in P will cause deformations and fractures at the points of surface contact and consequently, the block will begin to move

Limiting static frictional force Fs is directly proportional to the resultant normal force N

Fs = μsN



Theory of Dry Friction Constant of proportionality μs is known as

the coefficient of static friction When the block is on the verge of sliding,

the normal force N and the frictional force Fs combine to form a resultant Rs

Angle Φs that Rs makes with N is called the angle of static friction

sss

s N

N

N

F 111 tantantan



Theory of Dry Friction

Typical Values of μsContact Materials Coefficient of Static Friction μs

Metal on ice 0.03 – 0.05

Wood on wood 0.30 – 0.70

Leather on wood 0.20 – 0.50

Leather on metal 0.30 – 0.60

Aluminum on aluminum

1.10 – 1.70



Theory of Dry FrictionTabular Values of μs

Coefficient usually < 1 but for aluminum on aluminum, coefficient > 1

For coefficient > 1, frictional force > normal force

μs is dimensionless and depends on the characteristic of the contacting surfaces

When a more accurate calculation of Fs is needed, coefficient of friction is determined by experiments for the two materials involved



Theory of Dry FrictionMotion If the magnitude of P acting on the block is

increased so that it is greater than Fs, the frictional force at the contacting surfaces drops slightly to a smaller value Fs, called kinetic frictional force

The block will not be held in equilibrium (P > Fs) but slide with increasing speed



Theory of Dry Friction The drop made in the frictional force

magnitude, from Fs (static) to Fk (kinetic), can by explained by examining the contacting surfaces

When P > Fs, P has the capacity to shear off the peaks at the contact surfaces, causing the blocks to lift and ride on top of these peaks



Theory of Dry Friction Once the block begins to slide, high local

temperatures at these points of contact cause momentary adhesion (welding) of these points

Continued shearing of these welds is the dominant mechanism causing friction

Since resultant forces ∆Rn are aligned more in the vertical direction than before, they contribute smaller frictional components ∆Fn than when the irregularities are meshed



Theory of Dry FrictionResultant frictional force Fk is directly

proportional to the magnitude of the resultant normal force N

Fk = μkNConstant of proportionality μk is called

the coefficient of kinetic friction μk are typically 25% smaller than μs



Theory of Dry Friction Resultant Rk has a line of action defined

by Φk, angle of kinetic friction

Φs ≥ Φk

kkk

k N

N

N

F 111 tantantan



Theory of Dry Friction The graph summarizes the effects

regarding friction and shows the variation of frictional force F versus applied load P



Theory of Dry Friction Frictional force is categorized into three

ways- F is a static-frictional force if equilibrium is maintained- F is a limiting static-frictional force Fs when it reaches the maximum value needed to maintain equilibrium- F is a kinetic-frictional force Fk when sliding occurs at the contact surface



Characteristics of Dry Friction The frictional force acts tangent to the

contacting surfaces in a direction opposed to the relative motion or tendency for motion of one surface against another

The maximum static frictional force Fs that can be developed is independent of the area of contact, provided the normal pressure is not very low or great enough to severely deform or crush the contacting surfaces of the bodies



Characteristics of Dry Friction The maximum static frictional force is generally

greater than the kinetic frictional force However, if one of the bodies is moving with a

very low velocity over the surface of another, Fk becomes approximately equal to Fs

When slipping at the surface of contact is about to occur, the maximum static frictional force is proportional to the normal force

When slipping is occurring, the kinetic frictional force is proportional to the normal force

Engineering Mechanics: Statics Chapter 8: Friction Chapter 8: Friction.

Documents

concept of dry friction

normal forces

frictional force fn

normal force nn

force p

screwsfrictional forces

disksfrictional forces

surfaces of contact