Friction and Lubrication in Mechanical Design Episode 2 Part 5 doc

K = constant for the material lubricant combination 8.6.2 Mechanism for Surface Crack Initiation It is generally accepted that the penetration of asperities causes plastic deformation i

where

K = constant for the material lubricant

f = coefficient of friction

W,, = normal load per unit length

b = width of the contact band

Y , , V2 = surface velocities

C , , C2 = constants of materials which are the square root of the product of the

thermal conductivity, specific heat, and density

A modification of Blok’s formula was proposed by Kelly [15] for similar

materials with consideration of surface roughness The formula is given as:

where

TT = total surface temperature

TB = material bulk temperature

S = rms surface roughness (pin.)

K = constant for the material lubricant combination

8.6.2 Mechanism for Surface Crack Initiation

It is generally accepted that the penetration of asperities causes plastic deformation in the surface layers where the yield point is exceeded at the real area of contact Below the plastically compressed layer are layers under

elastic compression As soon as the asperity moves, the elastically com-

pressed layers will exert upon the plastic layer a force, which will create in

it a state of tension Consequently, tensile stresses will appear on the surface

in such conditions

The sliding motion also generates a temperature field, which pene- trates the surface layers The maximum temperature occurs at the contact surface and decreases with increasing distance from the surface as dis- cussed in Chapter 5 Accordingly, the surface layer is thermally elongated more than the subsurface layers and will experience compressive stresses

Wear 331

imposed by the bulk material If this compressive stress exceeds the yield stress, then a tensile residual stress will be induced in the surface after cooling It should also be noted that the temperature at the real area of contact can be very high at high sliding speeds which results in reducing the yield strength significantly and thus, increasing the stressed zone The tensile thermal stress on the surface can be calculated from [ 161:

coefficient of thermal expansion

pressure on the real area of contact

As illustrated by the parametric analysis in Chapter 5, the physical, chemical, and thermal properties of the lubricant can have significant influ- ence on the maximum surface temperature These properties control the amount of separation between rubbing surfaces and the thermal properties

of the chemical layers generated on them

8.7 DELAMINATION WEAR

Delamination wear denotes the mechanism whereby material loss occurs as

a result of the formation of thin sheets (delaminates) with thickness depen- dent on the normal load and the coefficient of friction The sequence of events which leads to the delamination can be summarized as follows: Surface tractions applied repeatedly by asperity action produce subsur- Cracks are nucleated below the surface

Further loading causes the cracks to extend and propagate joining The cracks propagate parallel to the surface at a depth governed by the After separation from the surface laminates may be rolled due to the

face deformation

neighboring ones

material properties and the coefficient of friction

sliding action to form wear debris

A comprehensive analysis of delamination wear can be found in Ref 17

Abrasive or cutting wear takes place when hard particles are present between the rubbing surfaces Such particles include metallic oxides, abra- sive dust, and hard debris from the environment These particles first pene- trate the metal and then tear off relatively large particles from the surface It

is one of the most common forms of wear and can be manifested in scratch- ing marks or gouging of the surfaces [ 18, 191

The load and the size of the abrasive particles relative to the thickness of the lubricating film are major factors which affect the weight loss by abra- sive wear The equation for abrasive wear can be expressed as:

Wear 333

Representative values for k given by Rabinowicz are tabulated below:

It should be noted the abrasive wear may result from, or can be accel- erated by, the wear particles themselves Wear particles for unlubricated steel can be as large as 50pm in size For well-lubricated steel, they are in the order of 2-3 pm Clearance between well-lubricated surfaces should be at least 4pm in order to allow the wear particles to leave the contact region

Corrosive or chemical wear takes place when the environmental conditions produce a reaction product on one or both of the rubbing surfaces and this chemical product is subsequently removed by the rubbing action A com- mon example is the corrosive wear of metals in air, which usually contains humidity and other industrial vapors Oxides or hydroxides of the metals are continuously formed and removed Carbonates and oxycarbonates may also occur from the normal CO2 present in the air Chlorides and oxychlorides are known to occur in industrial environments or in near-ocean operations The use of an appropriate lubricant can inhibit the corrosion mechan- ism and provide the necessary protection in a corrosive environment On the other hand, the lubricant itself may contain chemical elements, which react with the metals The degree of effectiveness of the lubricant in reducing corrosive wear will depend on its chemical composition and the amount

of dissolved water which may naturally exist in it

An example of intentionally inducing corrosive wear to prevent a more severe condition of surface damage is the use of extreme pressure (EP)

additives in the lubricant This is a common practice when scoring, galling,

or scuffing is to be expected The EP additive reacts with the surface at the locations where high pressures and high speeds create high temperatures and consequently catastrophic galling or seizure are replaced by mild corrosive wear References 20-26 contain more details and experimental data on the subject for the interested reader

8.10 FRETTING CORROSION

This type of surface damage generally occurs in mechanical assemblies such

as press fits and bolted joints due to the combination of high normal pres- sure and very small cyclic relative motion It is characterized by discolora- tion of the mating surfaces and wearing away of the surfaces

Many examples can be cited in the literature of the existence of fretting corrosion in machine parts and mechanical structures [27-331 It is reported

to be influenced by the hardness of the materials, the surface temperature, the coefficient of friction, humidity, lubrication, and the chemical environment

One of the early empirical formulas is that proposed by Uhlig [30] as:

a = slip distance (in.)

ko, k , k2 and constants

The constants for his data are:

ko = 5.05 x 10-6, kl = 1.51 x 10-*, k2 = 4.16 x 10-6

Measures, which can be used to reduce fretting include the minimization of the relative movement, reducing friction, use of an appropriate dry or liquid lubricant and increasing the surface resistance to abrasion

Cavitation is defined as the formulation of voids within or around a moving liquid when the particles of the liquid fail to adhere to the boundaries of the passage way It can produce erosion pitting in the material when these voids collapse Cavitation was first anticipated by Leonard Euler in 1754 to occur

in hydraulic turbines It is known to occur in ship propellers operating at

r = radius of the bubble

and Pi equals the vapor pressure

The capillary energy E of the bubble can also be expressed as:

where

ro = radius of the bubble before collapse

This energy of collapse is generally considered to be the cause of cavitation erosion pitting and wear

Erosive wear occurs due to the change of momentum of a fluid moving at high speed It has been observed in the wear of turbine blades and in the elbows of high-speed hydraulic piping systems In its extreme condition, erosive wear is the mechanism utilized in water jet cutting systems The change in the fluid particle velocity (A V) as it impinges on the metal surface can create a high impact pressure which is a function of the density of the fluid and the modulus of elasticity of the impacted material [37, 381 The

effect of the high pressures on wear is partly enhanced by the shearing action

of the liquid as it flows across the surface

The pressure generated due to the change in velocity can be quantified as:

P = ( A V ) &

where

P = impact pressure

E = modulus of elasticity of the material

p = density of the material

Surface damage due to erosive wear can be reduced by elastomer coating [39] and cathodic protection [40] The latter process causes hydrogen to be

liberated and to act as a cushion for the impact

Erosive wear is used to advantage in the cutting, drilling, and polishing

of brittle materials such as rocks The erosive action can be considerably enhanced by mixing abrasive particles in the fluid Empirical equations for the use of water jets with and without abrasives in cutting and drilling are given later in the book

Hays, D., Wear Life Prediction in Mechanical Components, F F Ling Ed.,

Industrial Research Institute, New York, NY, 1985, p.5

Kragelski, I V., Friction and Wear, Butterworths, Washington, D.C., 1965

Archard, J F., “Contact and Rubbing of Flat Surfaces,” J Appl Phys., Vol

24, 1953

Archard, J F., and Hirst, W., “The Wear of Metals Under Lubricated

Conditions,” Proc Roy Soc., 1956, A 236

Barwell, J T., and Strang, C D., “On the Law of Adhesive Wear,” J Appl

Mechanical Design and Power Transmission Special Report, Prod Eng., Aug

IS, 1966

Bayer, R G., Shalkey, A T., and Wayson, A R., “Designing for Zero Wear,

Mach Des., Jan 9, 1969

Bayer, R G., and Wyason, R., “Designing for Measureable Wear,“ Mach Des.,

Aug 7, 1969

Blok, H., “Les Temperatures de Surfaces dan les Conditions de Craissage sans

Pression Extreme,” Second World Petroleum Congress, Paris, June 1937

Blok, H., “The Dissipation of Frictional Heat,” Appl Scient Res., Sec A,

1955, Vol 5

Kelly, B W., “A New Look at Scoring Phenomena of Gears,” SAE Trans.,

1953, Vol 61

Barber, J R., “Thermoplastic Displacement and Stresses Due to a Heat Source

Moving over the Surface of a Halfplane,” Trans ASME, J Eng Indust., 1984,

Uhlig, H H., Corrosion Handbook, J Wiley, New York, NY, 1948

Evans, U R., Corrosion Protection and Passivity, E Arnold, London, England, 1946

Avery, H S., Surface Protection Against Wear and Corrosion, American Society for Metals, 1954, Chapter 3

Larsen, R G., and Perry, G L., Mechanical Wear, American Society for Metals, 1950, Chapter 5

Godfrey, D., NACA Technical Note No 2039, 1950

Wright, K H., Proc Inst Mech Engrs, London, l B , 1952, p 556

Row, C N., “Wear - Corrosion and Erosion, Interdisciplinary Approach to

Liquid Lubricant Technology,” NASA, SP-3 18, 1973

Almen, J O., “Lubricants and False Brinelling of Ball and Roller Bearings,” Mech Eng., 1937, Vol 59, pp 415422

Temlinson, G A., Thorpe, P L., and Gough, J H., “An Investigation of

Fretting Corrosion of Closely Fitting Surfaces,” Proc Inst Mech Engrs, Campbell, W E., “The Current Status of Fretting Corrosion,” ASTM Technical Publication, No 144, June 1952

Uhlig, H H., “Mechanism of Fretting Corrosion,” J Appl Mech., 1954, Vol

21(4), p 401

Waterhouse, R B., “Fretting Corrosion,” Inst Mech Engrs, 1955, Vol

Kennedy, N G., “Fatigue of Curved Surfaces in Contact Under Repeated Load Cycles,” Proc Int Conf on Fatigue of metals, 1956, Inst Mech Engrs, Sept

Oding, I A., and Ivanova, V S., Fatigue of Metals Under Contact Friction,” Proc of Int Conf on Fatigue of Metals, Inst Mech Engrs, 1956, pp 408413

Poulter, T C., “Mechanism of Cavitation-Erosion,” J Appl Mech., March

1942

1939, Vol 141, pp 223-249

169(59), pp 1157-1 172

1956, pp 282-289

35 Nowotny, H., “Destruction of Materials by Cavitation,” V.D.I., May 2, 1942,

40 Plesset, M S., “On Cathodic Protection in Cavitation Damage,** J Basic Eng.,

1960, Vol 82, p 808

Case Illustrations of Surface Damage

The factors influencing gear surface failures are numerous, and in many cases their interrelationships are not completely defined However, it can

be easily concluded that the gear materials, surface characteristics, and the properties of the lubricant layer are to a great extent responsible for the durability of the surfaces

It is widely accepted that pitting is a fatigue phenomenon causing cracks

to develop at or below the surface It is also known that lubrication is necessary for the formation of pits [l] The dependence of pitting on the ratio of total surface roughness to the oil film thickness is suggested by Dawson E2-41

Wear has been explained as a destruction of the material resulting from

repeated disturbances of the frictional bonds [5] Reduction or prevention or

wear may be accomplished by maintaining a lubricant film thickness above a certain critical thickness [6] Recent work in elastohydrodynamic lubrication [7-191 makes it possible to predict the thickness of the lubricant layer and the pressure distribution within the layer Scoring is believed to be a burning

or tearing of the surfaces This tearing is caused by metal-to-metal contact at high speed when the lubricant film fails and cannot support the transmitted load The failure of the lubricant film has been attributed to a “critical temperature” of the lubricant [20] Experimental evidence shows that the lubricant failure for any particular lubricant-material combination occurs at

a constant critical temperature [21, 221

339

9.1.1

Surface damage in gear systems is influenced by the following variables: load intensity, geometry of the contacting bodies, physical properties of the sur- faces, rolling and sliding velocities, properties of the lubricant, presence of abrasive or corrosive substances, existence of surface layers and their che- mical composition, surface finish, and surface temperature According to the elastohydrodynamic theory [7-191, most of these variables also govern the thickness of the lubricant film, which suggests that the major role is played

by the lubricant layer in the control of surface damage

The first step in structuring a design system is to identify the significant

parameters affecting the design The fundamental parameters for the pro- blem under consideration will be taken as:

The Significant Parameters for Surface Damage

Load intensity W , normal to the surface;

Oil inlet temperature To;

Lubricant viscosity at To ( P O ) ;

Effective modulus of elasticity of teeth E‘ = l/[(l/E,) + (l/E2)];

Effective radius of curvature at contact R’ = l/[(l/Rl) + (1/R2)];

Rolling and sliding velocity of teeth in contact U , V ;

Surface finish S;

Pressure coefficient of viscosity of the lubricant a;

Pressure-temperature coefficient of viscosity y;

Thermal properties of the tribological system

There are certain groups of these parameters, which are believed to collec- tively affect surface damage The most important of these groups are the Hertzian contact stress, the lubricant film thickness, and the maximum localized temperature rise in the film Simplified expressions, which can be used for these groups are:

Maximum Hertzian stress:

Maximum temperature rise:

A T 2 (0.0036) (,<! - s) W3/4Nj12 (9.2) Minimum thickness of lubricant film:

h = (2.5 x IO-’)R’(B x 106)”

Case Illustrations of Surface Damage

Although there is no uniformity of opinion on the nature of the role played

by the Hertzian-type stress field in surface damage, there is general agree- ment between investigators that the maximum Hertzian stress is a significant parameter, whose value should be kept within certain bounds if damage to the surface is to be avoided The pressure distribution in the oil film between lubricated rollers is also believed to conform closely to the Hertzian stress distribution The derivation of the equation for calculating the maximum Hertzian stress, Eq (9.1), can be found in many texts The explanation for

Eqs (9.2) and (9.3) is given in the following It should be noted that the

above expressions are intentionally simplified to facilitate the illustration of

the design procedure Among the important factors neglected in these equa- tion are the load distribution across the contact, the errors and the elastic deflection of the teeth, and the effect of the variation of the coefficient of

friction on the maximum temperature rise

9.1.2 Maximum Oil Film Temperature

The temperature rise in the oil film is calculated according to AGMA guide

for Aerospace Spur and Helical Gears

p,, = radius of curvature for pinion tooth

pG = radius of curvature for gear tooth

mG = gear ratio