Friction and Lubrication in Mechanical Design Episode 1 Part 6 pdf

They analyzed the contact between rough spheres by a physical model of a smooth sphere with the equivalent radius of both spheres pressed against a rough flat surface where the asperity

The Contact Between Rough Surfaces 105

The results as generated from the simulation for cutting conditions covering the practical range of applications are used in a regression analysis to obtain the best fit for the equation parameters C , k , , k Z , k3, and k4

The values of the system parameters of Eq (4.3) for the case of a chuck

mass (M,) of 34kg and machine structures with stiffness K , greater than 10' N/m were found to be independent of K , and are only dependent on the

uncoupled tool natural frequency, (5

All the simulated results were curve-fitted to give the following equations:

where

C;, = natural frequency of tool assembly (Hz)

These equations are applicable for the following conditions when K, is

greater than 10' N/m:

6lm/min < V < 305 m/min 0.127 mm/rev < f < 0.88 mm/rev 0.31 mm -= d < 0.71 mm

The interactions between the two bodies at the real area are what determines the frictional resistance and wear when they undergo relative

The Contact Between Rough Surfaces 107

sliding Even in the case of a Hertzian contact, the pressure distribution is not continuous Due to surface roughness it occurs at discrete points, and the force between the bodies is the sum of the individual forces on contacting asperities which constitute the pressure distribution An interesting investi-

gation of this problem was conducted by Greenwood and Tripp [30] They

analyzed the contact between rough spheres by a physical model of a smooth sphere with the equivalent radius of both spheres pressed against a rough flat surface where the asperity heights follow a normal Gaussian distribution about a mean surface, as illustrated in Fig 4.4a They further assumed that the tops of the asperities are spherical with the same radius and that they deform elastically according to Hertz theory The forces on the aspe- rities constitute the loading on the nominal smooth bodies whose deforma- tion controls the extent of the asperity contacts The problem is solved iteratively until convergence occurs

Assuming that the radius of the asperities is p, the radius of the contact on top of an asperity due to a penetration depth @can be calculated as (Fig 4.4b):

and the corresponding area of contact

From the Hertz theory, the load on the asperity can be calculated as:

where

E , , E2 = elastic moduli for the two materials

u l , u2 = Poisson's ratios for the materials

If z is the height of the asperity and U is the distance between the nominal

surfaces at that location, it can be seen from Fig 4.2b that o = z - U

Assuming a height distribution probability function $(z), the probability that an asperity is in contact at any location with nominal separation U can

be expressed as:

00

prob(z =- U) = $(z)dz

108 Chapter 4

Figure 4.4 (a) Nominal surfaces and superimposed asperities (b) Contact between rough surfaces - asperity contact

The expected force is:

If the asperity density is assumed to be q, the expected number of asperities

to be in contact over an element of the surface (&), where the separation between the nominal surfaces is U can be expressed as:

The Contact Between Rough Surfaces 109

The expected area of contact:

0

0

Asperity penetration U* = - Separation of nominal surface at any location h = fi

110 Chapter 4

T = dimensionless total load = 2 P/o E , m

p = dimensionless roughness parameter = qa,/ZX$

qf, = dimensionless average contact pressure =

Numerical results are presented in Greenwood and Tripp [30] based on the

previous analysis from which the following conclusions can be stated:

1 Load has remarkably small effect on the mean real pressure on top of the asperities This is illustrated by the numerical results given in Fig 4.5

Consequently the mean real area of contact is approximately linearly dependent on the applied load

The proportionality constant between the real area and load increases with increased root mean square (r.m.s.) roughness

(a) decreased asperity density and decreased raidus of the aspe- rities

The effective radius of the area over which the pressure is spread

is considerably larger than the Hertzian contact radius for low loads and approaches the Hertzian contact condition for high loads Consequently, the average mean pressure is considerably lower than the Hertzian pressure for low loads and approaches it for high loads This is illustrated in Fig 4.6

2

3

4

It is interesting to note that the first two conclusions are the same as

those noted by Bowden and Tabor [31] and the electric contact resistance measurements reported by Holm [32] The constant value of the average

pressure on the real area of asperity contact was assumed to be the yield stress at the asperity contacts However, the analysis presented by Greenwood and Tripp discussed in this chapter provides a rational proce-

The Contact Between Rough Surfaces

RELATIVE MOTION

It has been shown in the last section that the contact between elastic bodies with rough surfaces occurs at discrete points on the top of the asperities The interaction takes place at surfaces covered with thin layers of materials, which have different chemical, physical, and thermal characteristics from the bulk material These surface layers which unite under pressure due to the influence of molecular forces, are damaged when the contact is broken by relative movement During the making and breaking of the contacts, the

The Contact Between Rough Surfaces I13

underlying material deforms The forces necessary to the making and break- ing of the contacts, in deforming the underlying material constitute the frictional resistance to relative motion It can therefore be concluded that friction has a dual molecular-mechanical nature The relative contribution

of these two components to the resistance to movement depends on the types of materials, surface geometry, roughness, physical and chemical properties of the surface layer, and the environmental conditions in which the frictional pair operates

Molecular resistance or adhesion between surfaces is a function of the real

area of contact and molecular forces which take place there A theoretical

relationship describing the effect of the molecular forces can be given as:

where

h = Planck’s constant = 6.625 x 10-27 erg-sec

c = speed of light

I = distance between the contacting surfaces

m, n, e = mass, charge, and volume density of electrons in the solid

Adhesive forces are generally not significant in metal-to-metal contacts where the surfaces generally have thin chemical or oxide layers It can be significant, however, in contacts between nonmetals or metals with thin wetted layers on the surface as well as in the contacts between microma- chined surfaces

The role of roughness in the frictional phenomena has been a central issue since Leonardo da Vinci’s first attempt to rationalize the frictional resis- tance His postulation that frictional forces are the result of dragging one body up the surface roughness of another was later articulated by Coulomb This rationale is based on the assumption that both bodies are rigid and that

no deformation takes place in the process

I I4 Cii up I c r 4

Figure 4.7 Surface waves generated by asperity penetration

A modern interpretation of the mechanical role of roughness is based on the elastic deformation of the contacting surfaces due to asperity penetra- tion The penetrating asperity moving in a tangential direction deforms the underlying material and gives rise to a semi-cylindrical bulge in front of the

identor which is lifted up and also spreads sideways as elastic waves This is

diagrammatically illustrated in Fig 4.7 The size of the bulge depends on the relative depth of penetration w/p where w is the penetration depth and B is the radius of the asperity The process is analogous to that of the movement

of a boat creating waves on the water surface According to this theory the energy dissipated in the process of deforming the surface is the source of the mechanical frictional resistance and the surface waves generated are the source of frictional noise

4.7 FRICTION AND SHEAR

Both friction and shear represent resistance to tangential displacement In the first case, the traction resistance is on the surface or "external" to the

The Contact Between Rough Surfaces I15

Table 4.2 Friction and Shear

Traction Contact Direction of material Characteristic of

Friction External Discrete Perpendicular to the Sinusoidal waves Shear Internal Continuous Parallel to the Laminar

movement movement

body In the case of shear, the resistance is “internal” in the bulk material A

comparison between the two phenomena can be summarized in Table 4.2

It should also be noted that friction occurs when the strength of the surface layers is lower than the underlying layers On the other hand, if the surface layers are harder to deform than the underlying layers, it is expected that shear would occur In other words, friction can be associated with a

“positive gradient” of the mechanical properties with depth while shear can

be associated with a “negative gradient” of the material properties with

depth below the surface As illustrated in Fig 4.8, the former causes gradual

destruction of the surface layer with severity depending on the number of

passes that one surface makes on the other A negative gradient of the

strength of the surface layer would result in rapid destruction of the bulk material which occurs at the depth where the strength of the material is below what is necessary to sustain the tangential load

4.8 RELATIVE PENETRATION DEPTH AS A CRITERION FOR THE CONTACT CONDITION

An identor with spherical top is assumed in order to develop a qualitative criterion for the effect of the depth of penetration on the stress condition on

Figure 4.8 Effect of shear strength gradient on surface damage (a) dr/dh >

0, destruction of surface layer (b) dt/dh < 0, destruction of bulk material

I16 Chapter 4

the surface The model can be applied on a microscale where the identor is

an asperity, or a macroscale where the indentor is a cutting tool with a spherical radius Assuming homogeneous materials and applying the Hertz theory, the following relationships can be written:

a = radius of contact area

R = radius of the identor

P = applied load

E = effective modulus of elasticity

The relative penetration depth can therefore be expressed as:

Substituting for Pi3 from:

The above equation shows that the relative depth of penetration can be used

as a dimensionless parameter for evaluating the severity of the contact and

its transition from elastic to plastic to cutting Figure 4.9 gives an illustration

of utilizing the penetration ratio for this purpose [32]

4.9 EFFECT OF SLIDING ON THE CONTACTING SURFACES

The relative sliding between rough surfaces and the traction forces and frictional energy generated in the process result in a change in the tempera- ture and properties of the surface and the layers beneath it High thermal

The Contact Between Rough Surfaces I17

Figure 4.9 Effect of relative penetration of severity of contact (a) Elastic contact:

h / R -= 0.01 ferrous metals; h / R < 0.0001 nonferrous metals (b) Plastic contact:

h / R < 0.1 dry contact; h / R -= 0.3 lubricated contact (c) Microcutting: h / R =- 0.1

dry contact; h / R > 0.3 lubricated contact

flux can be expected at the asperity contacts for high sliding speeds, and the corresponding thermal gradients can produce high thermal stresses in the asperity and material layers near the surface Because of its importance, the thermal aspects of frictional contacts will be discussed in greater detail in the next chapter

The changes in the surface properties that occur include those caused by deformation and strain of the surface layer, by the increase in surface tem- perature and by the chemical reaction with the environment

Deformation at the surface may produce microcracks in the surface layer and consequently reduce its hardness The combination of compressive stress and frictional force and interaction with the environment can cause structural transformation in the surface material known as mechanochem- istry Also, a marked degree of plasticity may occur, even in brittle materi- als, as a result of the nonuniform stress or strain at the surface High microhardness may also occur immediately below the surface as a result

of sliding Its depth varies with the parameters contributing to the work- hardening process

It should be noted that if the contact temperature exceeds the recovery temperature (i.e., the recrystallization temperature of the alloy), the surface

I18 Chapter 4

layers become increasingly soft and ductile As a result, the surface becomes

smoother upon deformation Also, when two different metals are involved

in sliding, one of them softens while the other remains hard Transfer of metal occurs and one surface becomes smoother at the expense of the other The transfer of metal may occur on a microscale, as well as a macroscale The chemical interaction between the surface and the environment is an important result of the frictional phenomenon It is well known that appre- ciably deformed materials are easily susceptible to oxidation and chemical reactions in general The chemical layers formed on the surface can signifi- cantly influence the friction and wear characteristic, as well as the transfer of frictional heat into the sliding pair The chemical reaction can produce thin layers, which are generally very hard, on thick layers that are very brittle Oxide films formed on the surface can have different compositions depending

on the nature of the sliding contacts and the environmental conditions Steel surfaces may produce FeO, Fe304, or Fe2O3, and copper alloy surfaces can produce CuzO or CuO depending on the conditions [32, 331 For example,

hard Fe2) oxides (black oxide) can exist in the sliding contacts between rubber (or soft polymers) and a hard steel shaft in water pump seals They are known to embed themselves into the soft seal and cause severe abrasive wear to the hard shaft On the other hand, conditions can cause Fe304 (red oxide) to be formed which is known to act as a solid lubricant at the interface

Olsen, K V., “Surface Roughness in Turned Steel Components and the Relevant mathematical Analysis,” Prod Engr, 1968, pp 593606

Solaja, V., “Wear of Carbide Tools and Surface Finish Generated in Finish Turning of Steel,” Wear, 1958, Vol 2, pp 40-58

Ansell, C T., and Taylor, J., “The Surface Finish Properties of a Carbide and Ceramic tool,” Advances in Machine Tool Design and Research, Proceedings

of 3rd International MTDR Conference, Pergamon Press, New York, NY,