Friction and Lubrication in Mechanical Design Episode 2 Part 7 pdf

Case Illustrations of Surface Damage 381 Figure 9.23 load.. 388 Chapter 9 It is well known that during sliding contact, the frictional energy is transformed to thermal energy, result

380 Chapter 9

remain near normal The configuration of the joint is shown on Fig 9.22A

A schematic diagram is given in Fig 9.22B to show the animal’s leg in place with the static load and cyclic rubbing motion identified A special fixture is designed for applying constant compressive loads to the joint Fig 9.23 It has a spring-actuated clamp which can be adjusted to apply static

Case Illustrations of Surface Damage 381

Figure 9.23

load Constraining rig showing the fixture for application of compressive

loads between 450g and 3.6kg The spring is calibrated for continuous

monitoring of the normal load which is applied to the rat joint through a soft rubber pad

Test Specimens

The test specimens were all male white albino rats Their weight varies from

300 to 350g The rats were maintained on mouse breeder blox and water

The room temperature was kept between 80 and 84°F Nine rats were tested

in this study with each three specimens subjected to identical load levels

Test Plan

The right tibia of each rat was subjected to an alternating pull force between

0.0 and 90 g at a rate of 1500 cycles/min All the tests were conducted at this

value of the cyclic load with the compressive normal load fixed at 0.45, 0.9, and 1.8 kg, respectively The duration of the testing was 2-3 hr every day for

a period of 14 days After that period the rats were sacrificed and the

A typical variation of temperature on both the loaded and unloaded

joints is shown in Fig 9.24 The compressive load on the test joint is 1.8 kg

in this case The temperature on the test joint increased considerably during the first loading period The temperature rise tended to stabilize after the first week of test to an approximately 2S°F above that of the joint at rest The

latter showed no detectable change throughout the test Progressively lower temperature rise resulted in the tests with the smaller compressive forces These results are in general agreement with those obtained by Smith and Kreith [94] using thermocouples on patients with acute gouty arthritis, rheumatoid patients, as well as normal subjects during exercise and bed rest

9.6.3 Measurement of Changes in Mineral Content

The mineral content of the bone and the cartilage can be determined through the absorption by bone of monochromatic low-energy photon

Hours of Loading Figure 9.24 Sample of skin temperature data near the joints

Case Illustrations of Surface Damage 383

beam which originates in a radioactive source (iodine 125 at 27.3 keV) The

technique has been developed by Cameron and Sorenson [95]

The source and the detector system are rigidly coupled by mechanical means and are driven simultaneously in 0.025in steps in a direction trans- verse to the bone by a milling head attachment Measurements of the trans- mitted photon beam through the bone are made for a 1Osec interval after each stop and are automatically used to calculate the mineral content

A typical summary result is shown in Fig 9.25 where the change in bone

mineral ratio between the test joint and the one at rest are plotted as mea- sured at different locations below the surface In this case, the rat joint was subjected to a 1.8 kg compressive load for approximately three hours daily for a period of 14 days It can be seen from the figure that the tested joint showed a significantly higher mineral content ratio at 0.025in below the surface which gradually reaches 1 at a distance of approx 0.075in below the surface Progressively smaller increases in the mineral content ratio resulted from the lower compressive loads This result is interesting in view of the finding of Radin et al [88] that increased calcification and stiffening of the rabbit joints occurred as a result of repeated high impact load It shows that increased calcification can occur as well due to rubbing

of the joint under static compression

9.6.4

The surfiicc textiirt' and condition of the loaded and thc intact joints fiv each rat are in\.cstigated by riie;ins of' the biologicd microscope for gcncral ubscrvaticm histological slides for thc ccllular structiirc and tho scanning clect 1-011 111 icrosco pc for close in\w t iga tivn of' t tic load- b e x i ng ii t-ciis

At tlic end of c x i i test thc rat is sacrificed Thc joint is thcn dissectcd and put in fixative so that the cclIs rctain thcir shapc Thc tixatii'c iisccf is

0 I '!,,:) ~liitra-aldc.~i~,de When \.icnui iindcr ii biologiciil microscopc t o a

magnification 01 25 40 x considerable ~ e ; t r 01' tlic s m o o t h siirtiict's c m bc observed in thc loaded joint ;is sticnm in Fig 0.16 for ;i static compt-cssive

Investigation of Surface Characteristics and Cellular Structure

load o f 1.8 kg

The slides of the histology studies are prepared at four different sections

of the joint in both the tested and imniobilized joints The cellular structure

is compared as shown in Fig 9.27 for a conipressive load of 1.8 kg and the following differences are observed:

The procedure used for the electron microscope study of the structure of the cartilage is explained in detail by Redhler and Zimniy [96] The specimens from the cartilage are fixed in 0.1 ( X I glutra-aldehyde in Ringers solution The fixation takes approximately 4 hr They are then passed through graded

acetone The concentration o f the acetone is changed from 50, 70 90 and 100% for ;I duration of 0.5 hr each This is done t o ensure that no moisture exists which may cause cracking when coated with gold and palladium

alloys The magnification used is 1000 3OOOx and the areas seen :ire pri- marily load bearing ;ireas The differences observed among the loadcd, Fig 9.28 and the intact Fig 9.29 joints can be sunimrized in the following:

1 In the loaded specimens the zoning which predominates in the normiil cartilage disappears The upper surface is eroded and the radial pattern predominates throughout The relatively open mesh underneath the surfiice is replaced by ;I closely piicked

Figure 9.27

rest

Section of’ rat joint tcsted ( a ) under ;i 1.8 kg comprcssive load: (b) at

Figure 9.28 Electron microscope rcsults showing ( a ) surface roughness for joint

s u t j r c t c d t o 0.0 kg nc~rnial load: ( h ) surl'xc pits for joint subjected to I 8 kg COTII-

prcxsi\y loiid: (L*I surfiicc tear ror joint suh.iectod t o 0.9 kg compressive 10x1

network of thick c o m e fibers, all radial in direction ;is shown in Fig 9 2 k

The typc o f the s u r f i m of the intact cartilage Fig 9.29 suggests

ii trapped pool incchanisin o f lubrication The surtiicc is very smooth without serious asperities

The tibers in the intact citrtilage are oriented in a11 directions whcreas in the loaded cartilage they reorient theinseiiw in a radial form Fig 9.2Ka This is known t o he comnion in old, arthritic joints [97]

4 Deud culls can be seen under some of the loud-bearing areas Fig 9.28 Similar obsc.ri.ittions have been reported by McCall [97]

5 The surface r c ) i i g h n ~ s ~ o f the louded cartilage is drastically increiist'd This in turn causes further deterioration of the joint

9.28b and c

2

3

3s 7

Figure 9.29

Figs 9 2 h and c

(a) ( h ) Electron microscope results for the Joint at rest for thc rats of

9.7 HEAT GENERATION A N D SURFACE DURABILITY OF

RAMP-BALL CLUTCHES

9.7.1 Introduction

This section deals with the ttierm~il-reIat~d probleins and surface duriibility

of ramp ball clutches which arc gencrdly used for one-directional load transmission and ciin be iitilizcd In duvcloping mechanical function genera- tors Thc surfiice tcnipcrature rise undcr fluctuating load conditions is pru- dictcd by using a simplified one-dimensional t ransitlnt heat transfer model that is found t o be in good agreement with finite clement analysis The depth

of fretting wear due to repeated high-freqtrenq operation is t.valu:ited from the vicwpoint of frictional energy density A simplified niodel for fretting

\year due to fluctuation of Ioxi without gross slip in the wedging condition is proposed by qualitatively guiding the design of the clutch

388 Chapter 9

It is well known that during sliding contact, the frictional energy is transformed to thermal energy, resulting in high surface temperature at the contact [98, 991 If the high heat flux is periodic, the sharp thermal gradient might cause severe damage such as thermal cracking and thermal fatigue High temperature can also cause change of the material properties

of the surface layer, acceleration of oxidation, poor absorption of oil, and material degradation High temperature may also occur at the asperity contacts due to cyclic microslip, such as in fretting corrosion [lOO-l04]

In a rampball clutch (refer to Fig 930), the heat generated during its

operation can be classified into two categories:

Overrunning mode Usually the outer race rotates at a high speed with respect to the inner race during the overrunning mode The balls, under the influence of the energizing spring, will always contact both races and consequently produce a sliding frictional force This condition is similar to the case of lightly loaded ball bearing

Wedging mode The rampball clutch utilized in mechanical func- tion generators [105] can be ideally designed to operate on the principle of wedge During the wedging mode, the combination

of high oscillating pressure and microslip at the contact due to load fluctuation generates frictional heat on the surfaces of the balls and both races and, consequently may cause fretting-type damage This investigation focuses on the tribological behavior

in the wedging mode only because of its importance to the func- tion generator application

1

2

9.7.2 Analysis of the Wedging Condition

Many studies have been conducted on the temperature rise on the asperities during sliding and in fretting contacts [ 100-1041

Due to the nature of the contact and variation of Hertzian contact stress, the magnitude and the extent of the microslip area is a function of time However, because of the high stiffness of the clutch system, the windup

angle is very small; consequently the center of the contact area does not

move appreciably In order to simplify the analysis, the following assump- tions are made:

1

2

3

The contact area is a Hertzian circle area

The center of the contact area remains unchanged

Frictional heat is equally partitioned between the contacting sur- faces due to the existence of thin, chemical, surface layers with low conductivity

Figure 9.30

tact with wedging condition and corresponding hysteresis

( U ) Schematic o f B ramp-ball clutch (b) Schematic of fretting con-

4 All surfaces not in contact are adiabatic

According t o Mindlin's stick-slip model [ 1061 the contact area of sphere on a flat subjected to a tangential force is a mixed stick-slip circle

The boundary between the slip and stick regime is a circle with radius:

(9.26)

390 Chapter 9

where F is the oscillatory tangential force and g is the coefficient of friction

The stick circle shrinks with increasing tangential force, until the force

reaches a critical value, Fcr = N g At that instant, gross slip starts to occur

Within the contact area, the shear stress distribution is given by:

(9.27)

The amount of microslip in the slip annulus is found [107] as follows:

6(r) = 3(2 16Ga - [ [ 1 - ; sin-' (31 [ 1 - 2 ( y ] + $ $I-@},

(9.29)

The maximum microslip (when gross slip is impending) is obtained by set-

ting c = 0:

3(2 - V ) P N S(r) =

For the wedging contact of a ramproller clutch, the relation between the

normal load and tangential force at the upper interface can be expressed as:

Substituting Eq (9.31) into Eq (9.26) yields:

p(1 tans +cosa) r3

L ( * -

(9.31)

(9.32)

Equation (9.32) shows that the ratio of the radius of the stick circle to that

of the contact area is constant If the ramp angle is properly chosen, the

sphere will never slip, no matter how large the tangential force is

Case Illustrations of Surface Damage 391

Because no surface is perfectly smooth, the contact occurs only at dis- crete asperities and the real contact area is so small that it leads to extremely high local stress and high temperature rise under sliding condition The real contact area is approximately proportional to the normal load under elastic contact condition According to the Greenwood-Williamson elastic micro-

contact model [log], the average real contact pressure can be an order of

magnitude higher than the nominal contact pressure Accordingly, if the normal load is concentrated on the real contact area, the resulting stress and heat flux can be very high

9.7.3 Frictional Energy and Average Heat Flux

The frictional energy generated per unit time during fretting contact is the product of the interface shear stress (surface traction) and the amount of

microslip per unit time on each point within the slip annulus:

where

D = roller diameter = 2R,

a ( f ) = 0.881 E, for steel with Poisson's ratio U = 0.3 (9.34)

(9.35) (9.36)

Equations (9.36) and (9.37) in the wedging condition are plotted in normal-

ized form as shown in Figs 9.31 and 9.32, respectively The change of the c

value with increasing ramp angle can be readily seen in Fig 9.32

For the impending gross slip conditon, c = 0, Eq (9.32) gives:

tan a

Case Illustrations of Surface Damage 393

In this case, microslip occurs over the entire contact area and the corre- sponding deflection can be expressed as:

3(2 - u ) ~ N

1 6Gamax

Therefore, Eq (9.33) can be rewritten as:

In Eq (9.40), the double integral is the total tangential force, pZV(t), applied

on the ball Therefore, the energy rate can be expressed as:

where y1 is the number of balls; b is the ratio of the radii ( R i / R r ) ; R, and R,

are the radii of an inner race and the balls, respectively

Substituting Eq (9.38) into Eq (9.42) yields:

(9.43)

If the applied torque can be expressed as the product of its magnitude and a normalized continuous function of time as follows:

then, the frictional energy generated per unit time in the contact under

wedging conditions can be obtained by substituting Eq (9.44) into Eq (9.41):

(9.45)