Friction and Lubrication in Mechanical Design Episode 2 Part 12 potx

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 ‘oooo m 1 2 4 6 8 10 20 40 60 80100 150200 Velocity of Approach, V (ink) Figure 13.10 Ball displacement for impacts causing gross slip. (From Ref. 10.) 506 Chapter 13 Table 13.3 Pulse Characteristics N (Ib) vo (in./sec) U:’ Knax (W t (CLW ~~ 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. 13.3 VISCOELASTIC BEHAVIOR OF FRICTIONAL HERTZIAN 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 Figure 13.1 1 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 Figure 13.1 2 Diagrammatic representation of the test arrangement. 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 6V 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 f1”F. Two x-y plotters were used simultaneously to record the load-displace- ment and the displacement-time behavior of the ball under different load (41 7 42). regimes. As a general procedure, the apparatus was subjected to two consecutive hysteresis loops corresponding to the highest level of tangential load in all 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 Figure 13.1 3 (a) Load-displacement curves with 18.5 lbf normal force. (b) 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 7 DbpIacament Scab (in) - 012846 Loading Rata - 0.12261bf/s SeCOndr 111111111111111111111 (a) Time (8) 4 - 012a4s second8 Loading Rate 0.42 Ibfh I1111 IIIIIII 3 Figure 13.1 4 Displacement-time curves for 30 lb normal load. (a) 0.1225 lb/sec 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 0.0002 n C c Y 5 f 0 P I a I 0.0001 i 1 0 f a! al I o.Ooo0 I I 0.00000 o.oooo1 O.OOOO2 XI - Initial Cmp Dlsplrcement (In) Figure 13.1 5 Maximum creep versus initial creep rate. b a I 0.00003 Figure 1 3.1 6 Boltzmann model. 0.00015 CI g 0.00010 U f $ 0 Q P - 0.00005 0.00000 Time (8) Figure 13.1 7 time curves. Comparison between experimental and calculated displacenient- Figure 13.1 8 5 14 Diagrammatic reprcsentation of the experimental setup. [...]... corresponding to the maximum speed of the slider Figures 13 .21 and 13 .22 show sample results of the pressure distributions along the central line of the slider bearing in the direction of motion 5 18 Chapter 13 30 I 1 I 0 .25 0.50 0.75 I I I I I 25 = 20 r) P v 2 a e l5 Y) b 10 5 0 0.00 1.oo 1 .25 1.50 Location (In) Figure 13 .21 Pressure distribution along the central line in the direction of motion: h2 =... three transducers is given in Table 13.1 51 7 Some Experimental Studies Fsec 3.10 in 10 psi f Figure 13 .20 Sample experimental data: h2 = 0.000 6in. , m = 0.000 9in. /in. , 18 spm, SAE 5 oil, 25 °C at four different instances in time, as indicated by (a), (b), (c), and (d) in Fig 13 .20 The corresponding instantaneous velocities of the slider are also tabulated It was noticed during the tests that the peak... is schematically represented in Fig 13 .28 Standard bending fatigue test specimens (a) with 0. 125 in thickness are used throughout the test Liquid nitrogen is allowed to flow continuously from a container (b) with a controlled rate into a channel (e) and directed to the point where rapid induction heating is applied in an intermittent fashion This is accomplished by positioning the electrode (c) at an... loading screws which are mounted on the steel plate and apply the load to the pillowblocks The 52 I Some Experimental Studies 80 I I 1 5 10 15 60 f 0 0 v E 40 3 3 I 0 20 0 0 20 SpHd (in/ s) Figure 13 .24 Pressure-speed characteristic of slider bearing: h2 = 0.0010 in. , m = 0.001 1 in. /in. , SAE 20 oil, 25 °C steel plate and the loading screws are electrically insolated from the steel shaft to reduce possible... rise in all the performed tests 400 70 - 150 1 1 1 25 20 15 10 1 " 30 35 40 Load (Ibf) 60 80 100 120 140 160 Figure 13 .26 Experimental results of temperature versus load at different speeds: (a) SAE 80W90 oil; (b) residual compound; (c) water-miscible cutting fluid 25 0 n 22 00 t P 0 f 150 100 20 10 40 30 50 Lord (Ibf) I I I I 50 100 150 20 0 Load (N) (b) 300 - 130 120 - 0: 9080 Y c - 70 O 20 15 10 25 ... 0.4 to 1.3 m/sec (943-3 1 42 in. /min) Temperature and wear 520 Chapter 13 80 60 = 8 U e! 3 40 t Y) Q 20 0 0 5 10 8p.d 15 20 (ids) Figure 13 .23 Pressure-speed characteristic of slider bearing: h2 = 0.006 in. , m = 0.00 9in. /in. , SAE 5 oil, 25 °C data are given from tests with a heavy duty oil (SAE 80W-90), a highviscosity residual compound, a vegetable oil, and water-miscible cutting fluid (0.0476% emulsifiable... Experimental Studies 13.4 515 FILM PRESSURE IN RECIPROCATING SLIDER BEARINGS An experimental procedure for evaluating the oil film pressure in reciprocating 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... 133, and 178 N (10, 20 , 30, and 40 lbf) in succession without changing the point of load application The test speeds in this case are 300, 500, 750, and 1000 rpm The point of load application is changed after each constant speed test to a new location on the shaft Summary temperature data from the test with residual compound and water-miscible cutting fluid lubrication are shown in Figs 13 .26 b and c,... motion: h2 = 0.001 0in. , m = 0.0011 in. /in. , V = 18.01 in. /sec., p = 1.986 x 10-5 reyn 13.5 EFFECT OF LUBRICANT P O E TE ON TEMPERATURE R PRIS AND WEAR IN SLIDING CONCENTRATED CONTACTS The experimental study discussed in this section deals with investigating the effect of some of the physical properties of lubricants on the contact temperature and wear in heavily loaded Hertzian contacts under sliding conditions... bath temperature was maintained at 25 f 0.5"C 13.4 .2 Experimental Results A sample of the recorded data is shown in Fig 13 .20 The figure shows the pressure-position data for the test slider bearing when the SAE 5 oil is used at a speed of 18 spm In this case, the minimum film thickness is 0.006 in and the slope is 0.000 9in. /in It can be seen that for the first stroke, at the second and third oil holes, . 10 15 20 SpHd (in/ s) Figure 13 .24 m = 0.001 1 in. /in. , SAE 20 oil, 25 °C. Pressure-speed characteristic of slider bearing: h2 = 0.0010 in. , steel plate and the loading screws. displacement: pin.) 510 Some Experiment a1 Studies 51 I 7 DbpIacament Scab (in) - 0 128 46 Loading Rata - 0. 122 61bf/s SeCOndr 111111111111111111111 (a) Time (8) 4 - 012a4s second8. second8 Loading Rate 0. 42 Ibfh I1111 IIIIIII 3 Figure 13.1 4 Displacement-time curves for 30 lb normal load. (a) 0. 122 5 lb/sec loading rate; (b) 0. 42 lb/sec loading rate. 5 12 Chapter