Friction and Lubrication in Mechanical Design Episode 2 Part 12 pdf

The investigation described in this section, was therefore undertaken to study this “creep” phenomenon in the region below gross slip in static friction tests when the tangential loads a

Some Experimental Studies 505

values of d are then used to calculate & This kinetic coefficient of friction is also plotted against the striker velocity U in Fig 13.9 Its value is found to be

& = 0.22 and is independent of the normal force

Equation (13.13) is then used to obtain a theoretical plot of d versus U

beyond gross slip This is shown by the solid lines in Fig 13.10 The correla- tion between the calculated curves and the experimental data is evident The peak force and the time duration of the impact corresponding to gross slip are listed in Table 13.3 as a function of the normal force It can be

1 2 4 6 8 10 20 40 60 80100 150200

Velocity of Approach, V (ink)

506 Chapter 13

~~

15.25 4.35 5.75 1.321 9.57 74.1 30.5 7.75 11.7 1.511 19.47 64.8 45.75 10.95 17.5 1.600 29.10 61.2 61.0 13.4 22.6 1.686 37.6 58.8 91.5 18.7 34.0 1.818 55.6 53.9

easily seen that the coefficient of static friction based on the peak of the Hertzian pulse checks very closely with the value obtained from energy consideration It should be noted here, however, that the pulse duration

in this investigation varies between 0.35r, and 0.36r,, where r, is the equi-

valent natural period of the ball suspended on the frictional support, as calculated from:

At this ratio of pulse duration to natural frequency, the shape of the pulse is not of significant value and the transient response of the system is the same

as the static response to the pulse within the range of this test [13]

It is interesting to note that the gross slip coefficient of friction under impulsive loading is equal to 0.305 for the materials used and is independent

of the normal load for the range investigated This is more than three times higher than the corresponding value under static or vibrating loads The experimental results also show that at gross slip, the frictional joint undergoes a sudden drop in frictional resistance The frictional resistance in the gross slip region is substantially constant and corresponds to & = 0.22 All the energy applied during gross slip is dissipated

Figure 13.1 1 represents a dimensionless frictional force versus displace- ment plot which was found to be descriptive of the behavior of frictional contacts under impulsive loading

CONTACTS UNDER RAMP-TYPE LOADS

It has been observed during the tests described in the previous section, that considerable slip of a “creep” nature may occur under sustained loads with

Some Experimental Studies 507

impulsive loading Representation of frictional behavior of Hertzian contacts under

values below those necessary to produce ball accelerations which character- ize gross slip under such conditions

A phenomenon of “creep” in the frictional contact between a hemi-

sphere of lead and glass flats was detected by Parker and Hatch [14] during their studies on the nature of static friction Similar observations were also reported by Bristow [15]

The investigation described in this section, was therefore undertaken to study this “creep” phenomenon in the region below gross slip in static friction tests when the tangential loads are applied at relatively low rates and allowed to dwell for relatively short periods The utilized specimens and surface conditions are the same as those tested previously under vibratory and impulsive loads [ 161

13.3.1 Experimental Arrangement

The apparatus used in this investigation is schematically represented in Fig

13.12 A lf in diameter steel ball (a) is suspended between the two parallel

flat surfaces of two identical hear steel inserts (b), (c) Insert (b) is fastened to

a rigid steel frame (d), whereas (c) is fastened to a solid steel block (e) which

can slide tightly with minimum friction in the frame under the influence of

air pressure acting on a flexible diaphragm (f) The air pressure is controlled

508 Chapter 13

by a regulator and measured by means of a mercury manometer (g) Calibration of the normal force applied on the ball versus manometer read- ing is checked periodically by replacing the ball by a ring-type strain gage force meter of 14 in outer diameter The tangential load on the ball is applied by a special loading device capable of different rates of load appli- cation ranging from 0.12251b/sec to more than ten times this value The

device is composed of a lever (1) carrying a known weight (w) which can be

moved on the lever by means of a string on a rotating drum The rotation of the drum is controlled by pulleys driven by a variable-speed motor The position of the weight from the center of the lever is indicative of the tan- gential force on the ball This can be easily detected by the rotation of the

drum A variable resistance (r) connected to the drum was used in conjunc-

tion with a 6 V DC battery to produce a volage which is calibrated to

indicate the tangential force on the ball The calibration was done by utiliz- ing the ring-type strain gage force meter

The tangential force can be either applied to the ball or to the frame at the inserts by removing or inserting a pin (p) which disengages a special fork (h) to apply the load to the ball or to the frame, respectively This arrange- ment makes it convenient to evaluate the apparatus deformations and hys- teresis under any particular test condition before applying the tangential

Some Experimental Studies 509

load The ball displacement is measured by a differential transformer-type displacement transducer (t) rigidly fastened to the frame with the movable core in contact with the ball under a 12 g preload The transducer excitation and signal amplification is provided by a carrier-type preamplifier (s) coupled to a power amplifier which provides the input to the x-y plotters Accurate alignment is provided, ensuring that the load on the sphere is

on the same axis as the displacement transducer The whole apparatus is enclosed in a plastic box (n) which is thermostatically controlled to within

tests (approximately 121b) A third load cycle, similar to the expected fric-

tional cycle, was applied to the apparatus and recorded This cycle was found to give a reproducible hysteresis loop for the apparatus itself The pin (p) was withdrawn from the loading fork (h) and the particular load regime is then applied to the ball

The following are samples of the tests performed in this investigation In the test illustrated in Fig 13.13a, the ball was subjected to a 2 min dwell at a

load level of approximately 0.87 the gross slip value The load was then

released and reapplied until gross slip occurred The loading, unloading, and reloading up to gross slip were performed at the same rate The ball was repositioned and subjected to six successive hysteresis loops after a repro- ducible apparatus loop was obtained In the seventh loop the load was again sustained for 2 min at 0.87 the gross slip value, after which the load was

released and reapplied until gross slip occurred The figure shows strain- hardening effects in the successive loops with no significant change in the

“creep” displacement during the 2 min dwell

As shown in Fig 13.13b, the 2 min dwell tests were also performed at different load levels In each of the these tests, the load was sustained after two successive load cycles The load was released at the same rate, after which the ball was loaded to gross slip The data show an exponential increase in the creep displacement as the dwell load approaches the gross slip value Figure 13.13~ shows typical results from tests where the ball was sub- jected to several successive 2 rnin dwell cycles It can be seen that the “creep” displacement diminished with successive cycles The decay rate was found to

be more pronounced in the early cycles

Figure 13.14 shows typical time-displacement tests in which the load was applied at the particular rate and allowed to dwell at different points

t

Frictional loops at different load levels with 301b normal force (c) Successive dwell loops at the same load level with 50 lb normal force A: reproducible apparatus loop; B: frictional hysteresis loops (zero dwell); C: frictional hysteresis loops (2 min dwell); D: final frictional tests carried to gross slip (Force scale: 1 unit = 1.681bf

Ball displacement: pin.)

510

Some Experiment a1 Studies 51 I

loading rate; (b) 0.42 lb/sec loading rate

512 Chapter I3

within the region of gross slip The dependency of the creep displacement on the rate of ball displacement at the onset of dwell can be readily seen Figure 13.15 shows the plot of this relationship from the experimental data for normal loads of 30 and 501b, respectively The experimental results, as

illustrated by Figs 13.13a and b, indicate that the creep behavior of the frictional contacts (as in most low-temperature instances of creep) can be approximated by a Boltzmann model as shown in Figs 13.16, 13.17, and 13.8

The creep displacement can, therefore, be represented by [ 17, 181

where C is a characteristic constant when a linear model is assumed The factor C has been evaluated empirically by plotting the slope (xc)i

of the displacement-time curve at the onset of creep versus the total creep

displacement X, This can be done for any normal load, test temperature,

and rate of load application Figure 13.15 shows an example of such plots at 80°F with normal loads of 30 and 501b, respectively The points represent data from load application rates of 0.1225, 0.2667, and 0.421b/sec

The repeated “no-dwell” cycling tests at load levels below gross slip showed clearly that the largest plastic displacements occurred during the first cycle The area of the hysteresis loop diminished progressively with the number of cycles and the rate of decay of the loop area also decreased with the number of cycles Johnson [4] and O’Connor and Johnson [19] observed the phenomenon and attributed it to an increase in the local co- efficient of friction in the annulus of slip by the fretting action

These effects were observed by successive 2 min dwell cycles The tests also showed no significant dependence of the 2 min creep displacements on the number of no-dwell cycles which preceded them with the same maximum load

Gross slip curves, when produced without previous cycling history, exhibited considerably higher displacements in the region close to gross slip than expected by Mindlin’s theory [2, 31 Repeated cycling caused strain hardening and brought the load4isplacement curves closer to Mindlin’s prediction

Figure 13.17 shows the deviation of the experimental displacement-time curves from Mindlin’s theory at the lower loads and the accuracy of the linear viscoelastic model in describing the creep behavior It should be noted here that the values of the coefficient of friction at gross lip varied between 0.09 and 0.095 in most of the tests These values are essentially the same as those in the previous tests with vibratory loads

Some Experimental Studies 513

XI - Initial C m p Dlsplrcement (In)

Some Experimental Studies 515

13.4 FILM PRESSURE IN RECIPROCATING SLIDER BEARINGS

An experimental procedure for evaluating the oil film pressure in recipro- cating slider bearings with arbitrary geometry is presented in this section

[20] A special test fixture is constructed where the slider is inserted in such a

way as to insure that a specific film geometry is achieved and maintained throughout the test The pressure is monitored at three different locations along the central line of the slider by means of miniature pressure transdu- cers The setup is capable of producing oscillatory sliding motions with different strokes and speeds and can be used to simulate a variety of film geometries and operating conditions The results indicate the development

of negative pressure and cavitation during the return stroke The pressure distribution during the forward stroke follows the same pattern as that predicted by isoviscous theory The magnitude of the pressures, however, can be higher or lower than the isoviscous values depending on the operat- ing conditions The peak pressure during the forward stroke follows a square root relationship with the instantaneous sliding velocity, which can

be attributed to the thermohydrodynamic phenomenon discussed in

Chapter 6

13.4.1 Experimental Setup

The experimental setup is diagrammatically represented in Fig 13.18 The main components of the setup and a brief explanation of their functions are listed below:

A shaper carrier is used for providing the reciprocating motion, the

speed and stroke are adjustable

A slider block is used for holding the slider in order to maintain the film

geometry constant relative to the sliding surface The geometry is illustrated in Fig 13.19

A steel bar is used for transmitting the reciprocating motion from the

carrier to the slider It also serves as a cantilever spring to force down the brass surface of the slider block against the sliding sur- face

The slider surface is a well-ground steel plate The slider block is sub- merged in an oil bath The temperature of the bath is monitored by

a thermometer throughout the test

A potentiometer is used to record the position of the slider

A two-channel oscilloscope is used for monitoring the signals from the

A multichannel chart recorder is used for recording the signals pressure transducers

516 Chapter 13

Three temperature-compensated strain gauge transducers with a range

The minimum film thickness and slope of the slider is easily adjusted by changing the metal shims between the slider and the slider block Three oil holes of 0.0315 in diameter, which are located on the slider surface, allow the transducers to pick up the pressure The potentiometer is utilized to provide the information on change of position, and speed as a function of time For all the given data, the same film geometry is used with two speeds,

18 and 37 strokes per minute (spm), respectively The 18 spm produces a maximum speed of 9.17 in./sec when the slider is moving forward with an

11 in stroke The maximum speed corresponding to 37 spm is 18.07 in./sec with the same stroke The oil bath temperature was maintained at

It can be seen that for the first stroke, at the second and third oil holes,

an oscillatory pressure drop occurs before the peak pressure is reached A

sample of the pressure data from the three transducers is given in Table 13.1