Case Illustrations of Surface Damage 355 force effects of solid rollers cause an additional loading at the outer race contact (and a second-order, not significant unloading at the inner race con tact). Harris and Aaronson [40] made analytical studies of bearings with annual rollers to investigate the load distribution, fatigue life, and the skid- ding of rollers. Their work shows that hollow rollers increase the fatigue life of the bearing and decrease the skidding between the cage and roller set. They suggested that attention should be paid, however, to the bending stress of the rollers and to the bearing clearance. This section describes an experimental study undertaken by Suzuki and Seireg [41] to compare the performance of bearings with uncrowned solid and annular rollers under identical laboratory conditions. Bearing temperature rise and roller wear are investigated in order to demonstrate the advantages of using annual rollers in applications where skidding can be a problem. Test Bearings The two bearings used in the study have the same dimensions and configura- tions with the exception that one bearing has annular rollers and the other bearing has solid rollers. The details of the bearings are given in Table 9.1. Brass is selected as the roller material in order to rapidly demonstrate the effect of annular rollers on temperature rise, and roller wear. The ratio of the inside to the outside diameter of the hollow roller is taken as 0.3. Three sets of inner rings with different outside diameters are used for each bearing in order to produce the different clearances. Special efforts were undertaken in machining the rollers and rings to approach the dimensional accuracy and surface finish of conventional har- dened bearing steels. Test Fixture The experimental arrangement is diagrammatically represented in Fig.9.12. the two test bearings (a) and (b) (one with hollow rollers and another with solid rollers) were placed symmetrically near the middle plane of a shaft (c). The shaft is supported by two self-lubricated ball bearings (d) on both sides. A variable speed drive is used to rotate the shaft through a V-belt (e) and and a pulley (f) at one end of the shaft. The load is applied radially on the outer rings (g) inside which the bearing is placed by changing the weight (j) suspended at one end of a bar (k). The latter loads a fulcrumed beam-type load divider, which is especially designed to provide identical loads on both bearings. A strain gage ring-type load transducer (i) monitors the load applied on the test bearings to confirm the equality of the load on them at all times. Separate 356 Chapter 9 Table Q.1 Test Bearing Specifications Bearing outside diameter Bearing inside diameter Bearing width Outer race inside diameter Inner race outside diameter Roller diameter Roller length Number of rollers Roller inside diameter Diameter ratio Bearing radial clearance Roller material Outer and inner race material Surface finish for rollers and races 4.3305 in. 1.9682 in. 1.06 in. 3.719 in. 2.5658 in. 2.5637 in. 2.5620 in. 0.5766 in. 0.659 in. 12 0.1719 in. 0.3 0.0021 in. 0.0038 in. Brass Mild steel 8-10 pin rms (10.99947 cm) (4.999228 cm) (2.6924 cm) (9.4462 cm) (6.517132 cm) (6.51 1798 cm) (6.50478 cm) (1.464564 cm) (1.67386 cm) (0.436626 cm) (0.005334 cm) (0.009653 cm) Load Figure 9.1 2 Diagrammatic representation of experimental setup for dynamic test. Case Illustrations of Surface Damage 35 7 oil pans (1) are placed below each of the test bearings. Oil is filled to the level of the centerline of the lowest roller. Copper+onstantan thermocouples are used to measure the bearing temperatures as well as the oil sump tempera- ture. The bearing thermocouples are embedded 30" apart at 0.01 in. (0.25mm) below the surface of the outer rings where rolling takes place. The thermocouples are connected to a recorder (s) through a rotary selec- tion switch (q), and a cold box (r). Results Figure 9.13a shows the time history of the outer race temperature rise for the bearing with annular rollers. Steady-state temperature conditions are reached after approximately two hours. Figure 9.13b shows the bearing temperature rise as well as oil temperature rise at steady state conditions for a shaft speed of 1000 rpm. The temperature rise for both solid rollers and annular rollers are essentially the same at this speed. At speeds of 2000 rpm and 3000 rpm, on the other hand, the temperature with solid rollers is higher than that with annular rollers. The temperature rise differences are most pronounced at 2000 rpm. Wear Measurement The radioactive tracing technique used in the test is similar to that used by L. Polyakovsky at the Bauman Institute, Moscow for wear measurement in the piston rings of internal combustion engines. The test specimens (hollow or solid rollers) are bombarded by a high- energy electron beam emitting gamma rays. The strength of the bombard- ment is governed by the energy of the electron beam, the exposure time, and the material of the specimen. The radioactivity, which naturally decays with time, is also reduced with wear of the bombarded surface. The rate of reduction of the radioactivity is approximately proportional to the depth of wear. The amount of wear can therefore be detected by monitoring the radioactivity of the specimen and using a calibration chart prepared in advance of the test. The main advantage of this method is the ability to detect roller wear without disassembling the bearing. The disassembling process is not only time consuming, but it may also alter the wear pattern of the test specimens. In this study, one roller in each bearing is bombarded and assembled with the rest of the rollers. A scintillation detector (w) is placed on the outer surface of the outer ring of the bearing (Fig. 9.12) and a counter is used to monitor the change in radioactivity of the bombarded rollers. The diameter of rollers is periodically measured using an electric height gage to check the accuracy of the radioactive tracing technique. 358 60- E: 50- e w- 40- 2. 3 30- a 20- 10- 0 $- L Chapter 9 Bearing Oil I I I 1 I I 70 - . SAE50Oil I I 3000 60- Bearing Temperature - rpm 50- e a 40- 3 30- 8- I' Y Y - K loo0 !i 20: - - 0- - Q Q 2000 ______ x x "x 1000 E- 10- 0 1 I I I 1 .o 1.5 2.0 2.5 0.0 0.5 Time (hrs) Figure 9.13 (a) Temperature rise-time history for the bearing with annular roll- ers. (b) Temperature rise at steady-state conditions. The shaft speed for the wear test is selected as 3000 rpm and kept unchanged. SAE IOW oil is used as the lubricant for the test bearings to accelerate the roller wear. The bearing outer race temperature and oil tem- perature are monitored throughout the test. Figure 9.14a shows a comparison of the wear of the roIIers during the test. As can be seen from the figure, the wear of the annular rollers is Case Illustrations of Surface Damage 40 - 359 - - Sdid Roller Bearing -A- Annular Roiler Bearing o.oO06 1 1 Flgure 9.14 oil. (a) Roller wear. (b) Temperature difference between bearings and considerably lower than that of the solid rollers. It should be noted that after an initial running period of 30 hours, the oil was changed and a con- siderably lower rate of wear resulted. The wear rate during this phase of the test is shown as 5.7 x 10-7 in./h (14.5 x 10-6 mm/h) for the hollow roller as compared to 8 x 10-7 in./h (20.4 x 10-6 mm/h) for the solid roller. It was observed throughout the test that the wear detected using radio- active tracing technique is slightly higher than that measured directly using the electric height gage. The reason may lie in the fact that the wear detected by the radioactive tracing technique is an average wear, which includes the 360 Chapter 9 indentations due to local pittings or flakings. Consequently, if the interest is to study the effect of wear on the change of bearing clearance, it would be more appropriate to use the height gage for measuring the dimensional change. On the other hand, if the interest is to investigate the surface damage, the radioactive tracing technique would be a good tool for this purpose. Better accuracy can be expected with this technique when steel rollers are used. Gamma-ray emission is stronger with steel and conse- quently the influence of the radioactivity existing in the natural sp: :e on the results is reduced. The temperature rise in the bearings and oil during the wear est is shown in Fig. 9.14b. The temperature of the outer race of the solid roller bearing is shown to be consistently higher than that of the annular roller bearing at all times. It is interesting to note that the annular roller exhibited a small number of local pits scattered on the rolling surface. In the solid roller, however, a large number of pits were observed in the rolling direction only at the central region of the rolling surface. This may also be due to the cooling effect at the ends of the rollers. 9.3 SURFACE TEMPERATURE, THERMAL STRESS, AND WEAR IN BRAKES The high thermal loads, which are generally induced in friction brakes, can produce surface damage and catastrophic rotor failure due to excessive sur- face temperatures and thermal fatigue. The temperature gradients and the corresponding stresses are functions of many parameters such as rotor geo- metry, rotor material, and loading history. Due to the wide use of frictional brakes, an extensive amount of work has been undertaken to improve the performance and extend the life of their rotors. Some research has been aimed towards studying the effects of rotor geometry on the temperature and stress distribution using classical analyti- cal [42-45] or numerical [46-521 methods. Other studies have concentrated on investigating the effects of rotor materials on the performance of the brake [53-551. The efforts to improve the automobile braking system performance and meet the ever increasing speed and power requirements had resulted in the introduction of the disk braking system which is considered to be better than the commonly used drum system. A newer system which is claimed to be superior to both of its predecessors is now being introduced. The crown system [56] which can be viewed as a cross brake, with a drum rotor and a Case Il[ustrations of Surface Damage 361 disk caliper, combines the advantages of both drum and disk systems. It has the loading symmetry of the disk caliper which results in less mechanical deformation. It also has the larger friction surface areas and heat exchange areas of the drum which result in better thermal performance and lower temperatures. A study by Monza [56], in which the disk and crown are com- pared, indicated that more weight and cost reduction are attainable by using the crown system. Moreoever, under similar testing conditions, the crown rotor showed 10-20% lower operating tempratures than its counterpart. This section is aimed at investigating the thermal and thermoelastice performance of rotors subjected to different types of thermal loading. Although there are many procedures in the literature for the analysis of temperature and stress in brake rotors based on the finite element method [l, 3, 8, 91, these procedures would require considerable computing effort. Efficient design algorithms can be developed by placing primary emphasis on the interaction between the design parameters with sufficient or reason- able accuracy. Sophisticated analysis can then be implemented to check the obtained solution and insure that the analytical simplifications are acceptable. For the thermoelastic analysis in this section, a simplified one-dimen- sional procedure is used. The rotor is modeled as a series of concentric circular rings of variable axial thickness. Furthermore, it is assumed that the rotor is made of a homogeneous isotropic material and that the axial temperature and stress variations are negligible. The procedure first treats the thermal problem to predict the temperature distribution which is then used to compute the stress distributions. 9.3.1 This algorithm used to calculate the temperature rise is a simplified one- dimensional finite difference analysis. The analysis consideres the transient radial temperature variations and neglects both axial and circumferential variations. The rotor, which is subjected to a uniform heat rate, Qr at its external, internal or both cylindrical surfaces dissipates heat through its exposed surfaces by convention only. The film coefficient depends only on the geometrical parameters. The proposed analysis is based on the conservation of energy principles for a control volume. This can be stated as: Temperature Rise Due to Frictional Heating where Qin and Qour are the rate of energy entering and leaving the volume, by heat conduction and convection respectively and Qslorcd is the rate of 362 Chapter 9 energy stored in the volume. For the shaded element of Fig. 9.15, Eq. (9.4) with appropriate substitution becomes: where Qc,n and &+, are heat quantities entering and leaving the volume by conduction, and Qv,n and Qd,n are geometry dependent convection heat quantities entering and leaving the body depending on the surrounding temperature, T,. With a current temperature rise above room temperature, T,,, at the interface M, one can solve for the future temperature rise, at time t + 1, for the same location [57]: where k PC B = - is the thermal diffusivity v,n T ‘n C.L. 7 rIl-1 I 1 Figure 9.1 5 Diagram used for the temperature algorithm. Case Illustrations of Surface Damage 363 Similar expressions can be obtained for the temperature at the inner and outer surfaces. The temperature rise in the next time step at the outer radius is: (9.7) and the temperature rise in the next time step at the inner surface is obtained by replacing all the 2,O and U subscripts in Eq. (9.7) by m, i, and I, respectively. In the above equations Ao, A,, and A, are the cylindrical areas of the outer, inner, and interface surfaces, respectively. Au,, and are the ring side areas, upper, and lower halves. Ad,, is the area generated by the thick- ness difference between two adjacent rings (refer to Fig. 9.15). As can be seen, the above algorithm can easily be modified to allow for any variations in heat input, convective film, and surrounding temperatures with location and time. 9.3.2 The Stress Analysis Algorithm The geometrical model of this algorithm is identical to that of the tempera- ture algorithm. For this analysis, both equilibrium and compatibility con- ditions are satisfied at the rings interfaces. Considering the inner and outer sides of the interface rn+l of Fig. 9.16, the continuity condition (or strain equality) can be expressed as a function of the corresponding stresses as follows [58, 591: where 0 (of,n+l) , (of,n+,)’ = tangential stresses at the outer and inner side of interface r,+I, respectively 0 , (o~,~+~)’ = thermal stresses at the corresponding locations 364 Chapter 9 !I c 1- - In*' I Tl I m i rL.L. Figure 9.16 stress algorithm. Representation of the disk geometry and the notations used in the The radial stress sures on both sides of the interface, can be derived as: at the radius I-,,+~, which is the average of the pres- The tangential component o,,~+~ is calculated by averaging the stress on both sides of the interface as: (9.1 I) [...]... the Investigated Cases (2) (2) I Uniform thickness and 2 Uniform thickness and 3 Uniform thickness and sharing 4 Uniform thickness and sharing (2) = 0 .25 external loading internal loading equal load = 0.50 73,4 56. 4 27 2 ,28 3.7 70,378.9 137,739.3 50,5 06. 1 67 ,039.4 13 1, 164 .9 54,8 46. I 19 ,61 6.8 50 ,28 3.1 Load condition = 0.75 33,954 .6 16, 393.5 optimal load magnitudes This is due to the fact that the inner... Investigated Cases Table 9.4 (2) = 0 .25 Load condition 1 Uniform thickness and 2 Uniform thickness and 3 Uniform thickness and sharing 4 Uniform thickness and sharing external loading internal loading equal load optimal load ):( = 0.50 (2) = 0.75 73,4 56. 4 27 2 ,28 3.7 70,378.9 137,739.3 50,5 06. 1 67 ,039.4 13 1, 164 .9 54,8 46. 1 19 ,61 6.8 50 ,28 3.1 33,954 .6 16, 393.5 Chapter 9 368 Brakes without surface coating:... loading and material parameters are used in the considered cases: Geometry: Disk outer radius, ro = 12. 0in Disk inner radius, ri = 6. 0in Disk thickness, fmax = 12. 0 in  366 Chapter 9 Material: Density, p = 0 .28 6 lb /in. 3 Young's modulus, E = 30 x 106psi Coefficient of thermal expansion, a = 7.3 x 10 -6 in. / (in. OF) Thermal conductivity, k = 26 .0 BTU/(hr-ft-OF) Specific heat, c = 0.1 1 BTU/(lb-OF) Loading... 9 .2 The Maximum Temperatures ( O F ) for the Investigated Cases Load condition 1 Uniform thickness and external loading 2 Uniform thickness and internal loading 3 Uniform thickness and equal load sharing 4 Uniform thickness and optimal load sharing )( : = 0 .25 (2) = 0.50 ):( = 0.75 448.9 1345.8 465 .2 787.9 0.75 469 .8 724 .3 395 .2 543.8 338.9 29 5.9 3 02. 8 36 7 Case Illustrations of Suflace Damage Table... equation for this case is found to be: (9 .22 ) The correlation between the developed equation, Eq (9 .22 ), and the experimental data [71] is shown in Fig 9.18, 9.4.4 Equations for Slotting and Drilling by Abrasive Jets Equations (9 .20 ) and (9 .22 ) for deep slot cutting and hole drilling were extended for predicting the performance of abrasive jets A dimensionless modifying factor has been developed to account... expressed as: (z)r=(3°. 763 (E) 1 .27 8 (9 .23 ) The deep slot cutting equation by abrasive jets can be readily generated by combining Eqs (9 .21 ) and (9 .23 ) as: (9 .24 ) Similarly, the dimensionless drilling rate equation by abrasive water jets can be readily obtained by multiplying the plain water drilling equation, Eq (9 .22 ), with the abrasive factor: 8 6 -4 f N 1 s 6 U 2 0 r Ah 1 hw1Figure 9.1 9 The correlation... developed by Seireg and Kempke [93] for studying the behavior of in vivo bone under cyclic loading The load is applied to one joint while the other remains at rest The factors investigated include changes in surface temperature at the joint, surface damage, cellular structure, and mineral content in the cartilage and bone 9 .6. 1 The Experimental Apparatus and Procedure The apparatus used in this investigation... of the joint Radin et al [88-901 and Simon et al [91] have extensively investigated the effects of suddenly applied normal loads The experiment reported in this section [ 92] investigates the effects of continuous high-speed rubbing of the joint in vivo when subjected to a static compressive load which is maintained constant during the rubbing The patella joint of the laboratory rat was tested in a specially... (9 .20 ) In deep kerfing by water jets, a rotary head with a dual nozzle is generally required Because of the jet inclination angle @ and the combination of tangential and traverse velocities, Eq (9 .20 ) is modified and a generalized equation for water jet cutting using a rotary dual jet in deep slotting operations is developed as: ($).= 1 .22 2 x l o - y c o s(~ O 3 y ) - 3 4 1 (9 .21 ) where is the resultant... machines, and processors of bulk solids and fluids The use of vibration to reduce the ground penetration resistance to foundation piles was first reported in 1935 in the U.S.S.R Resonant pile driving was successfully developed in the U.K in 1 965 and proved to be a relatively fast and quiet method Case Illustrations of Surface Damage 377 Since the early 195Os, there has been increasing interest in the . in. 2. 565 8 in. 2. 563 7 in. 2. 5 62 0 in. 0.5 766 in. 0 .65 9 in. 12 0.1719 in. 0.3 0.0 021 in. 0.0038 in. Brass Mild steel 8-10 pin rms (10.99947 cm) (4.99 922 8 cm) (2. 6 924 cm). (2. 6 924 cm) (9.44 62 cm) (6. 5171 32 cm) (6. 51 1798 cm) (6. 50478 cm) (1. 464 564 cm) (1 .67 3 86 cm) (0.4 36 6 26 cm) (0.005334 cm) (0.00 965 3 cm) Load Figure 9.1 2 Diagrammatic representation. 27 2 ,28 3.7 137,739.3 67 ,039.4 3. Uniform thickness and equal load sharing 13 1, 164 .9 54,8 46. 1 19 ,6 16. 8 4. Uniform thickness and optimal load sharing 50 ,28 3.1 33,954 .6 16, 393.5 368