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 (crest 09 , Constant Compressive Force (static) -+/ Clamp Figure 9.22 Schematic representation of applied load and rubbing motion. 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 382 Chapter 9 different tests were performed on the joint. Only the temperature data were obtained while the rats were tested. 9.6.2 Temperature Measurements The temperature over the skin of the rat at the patella joint is measured by thermocouples. The combination used is iron and constantan and the tem- perature can be continuously recorded with an accuracy of fO. 1 OF. 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 901 I I I I I I I I I 0 2 4 6 8 10 12 14 16 18 20 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. 2.0 1.5 0 K c Q) z = 1.0 s Y 0.0 1 I I 0.05 0.10 0.15 0.20 Distance From Tibia Joint (in) Figure 9.25 Change in mineral content ratio below the surface. 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- bexi ng ii t-ciis. At tlic end of cxii 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 to a magnification 01. 25 40 x. considerable ~e;tr 01' tlic smooth siirtiict's cm 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 of 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: 1. 2. The surface is significantly rougher in the loaded joint as com- pared to the one at rest. The surfiice structure is compressed at some locations causing an increase in the mineral content. This observation is supported by the results of the photon absorption technique. 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 (XI glutra-aldehyde in Ringers solution. The fixation takes approximately 4 hr. They are then passed through graded acetone. The concentration of the acetone is changed from 50, 70. 90. and 100% for ;I duration of 0.5 hr each. This is done to 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 sutjrctcd to 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 to 0.9 kg compressive 10x1. network of thick come fibers, all radial in direction ;is shown in Fig. 9.2k. The typc of the surfim of the intact cartilage. Fig. 9.29. suggests ii trapped pool incchanisin of 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 to 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 rc)iighn~s~ of the louded cartilage is drastically increiist'd. This in turn causes further deterioration of the joint. 6. Pits and tears appear in the loaded citrtilaze ;IS illustrated in Figs 9.28b and c. 2. 3. 3s 7 Figure 9.29 Figs. 9.2h and c. (a). (h) Electron microscope results for the Joint at rest for thc rats of 9.7 HEAT GENERATION AND 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 to 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 of B ramp-ball clutch. (b) Schematic of fretting con- 4. All surfaces not in contact are adiabatic. According to 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) [...]... model [ 120 ] a viable approach for predicting wear depth Seireg and Hsue [ 121 ] indicate that the wear depth is dependent on the temperature rise and the heat input at the contacting surfaces Suzuki and Seireg [I 221 also provide evidence for the correlation between wear and energy input Due to the nature of fretting contact, the frictional energy can be accumulated within a limited area with minimum convection... of friction a = amplitude (center-to-peak) 1 = total number of cycles N The relation between wear depth and the energy input can then be obtained by curve fitting A linear fuction relating frictional energy density and Vickers hardness is found as: Q h = 0.1 47 H,, (9.60) where h = fretting wear depth H , = Vickers hardness I I I 1 I 1 I I 1 Torque =22 .6‘(1-cos (2* pi’ft)) /2 N-m =20 0’(1 -ws(P*pi’ft))l2... Eng Sci., 19 67, Vol 9(1) 5 Kragelskii, 1 V., Friction and Wear, Butterworths, 1965 6 Feng, I-Ming, and Chang, C M., “Critical Thickness of Surface Film in Boundary Lubrication, ” ASME J Appl Mech., September 1956, Vol 23 (3) 7 Cheng, H S., and Sternlicht, B., “A Numerical Solution for the Pressure, Temperature and Film Thickness Between Two Infinitely Long, Lubricated Rolling and Sliding Cylinders Under... Specific density (c) 4 3.8 mm (0.15 in. ) 2 x 10" N/m2 (30 x 106psi) 0.3 0 .23 ( b+ w, 45 W/(m-OC) (26 BTU/(hr-ft-OF)) 78 50 kg/m3 (490 lb/ft3) 0. 42 kJ/(kg-"C) (0.1 BTU/(lb-OF)) Assuming that the system is subjected to a periodic versed sine load: To =22 .6( 1 - cos 2x9)(N-m) the corresponding average heat flux during the microslip condition is plotted in Fig 9.33 9 .7. 4 Estimation of the Temperature Rise... 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 normalized 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 p(1 +cosa)... energy and fretting wear depth, the work by Sat0 [ 123 , 124 1 has been adapted In his series of experiments, carried out on a glass plate in contact with a steel ball of 5 mm (0 .2 in. ) diameter, Sat0 obtains good agreement with other researchers and suggests that the coefficient of friction increases steadily up to 0.5 as the microslip annulus grows After gross slip, amplitude = 3 pm ( 120 pin.) at 9.8 N (2. 2... 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 [1 07] as follows: 6(r) = 3 (2 16Ga - [[ ; 1- sin-' (31[ 1 -2 ( y ] + $ $I-@ (9 .29 )... frequency of 50 and 100 Hz, respectively By comparing the results with those from the one-dimensional theory, the difference is found to be relatively small in the first two cycles However, a stronger cooling effect results for longer load duration in the finite element method due to convection to the lubricant I 70 .4 - I r I I I I I I Torque =22 .6*(1-cos (2' pi'Pt)) /2 N-m =20 0'( 1-cos (2' pi'f9)) /2 Ib -in f=100... 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):... conditions Kayaba and Iwabuchi [ 1 121 report that fretting wear decreases with increasing temperature up to 300°C ( 570 "F), and the trapped debris is Fe304, which has a lubricating effect Fretting wear at high temperatures has been receiving particular attention [ 1 13-1 161 However, the results are inconsistent because of different materials, experimental conditions, and estimates of wear The influence of . I Torque =22 .6*(1 -cos (2& apos;pi'Pt)) /2 N-m =20 0'( 1 -cos (2& apos;pi'f9)) /2 Ib -in - f=100 HZ Figure 9. 37 The heat flux at four key points under the fretting contact. 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. 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