THE UN IVERSITY OF MI CHI GAN COLLEGE OF ENGINEERING Department of Mechanical Engineering Final Report RESIDUAL STRESSES IN HARDENED BEARING RACES, L, J. Quackenbush ORA Project 0713 5 under contract with: ~ FEDERAL-MOGUL CORPORATIQN DETROIT, MICHIGAN administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR January. 1966

IS Meagi45 u kV 4 15

TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS v ABSTRACT vii INTRODUCTION 1 I, SUMMARY AND INTERPRETATION OF RESULTS 2 IIo RESULTS OF DETAILED INSPECTION 6 III. ANALYTICAL PROCEDURES 31 Measuring Techniques 31 Stress Calculations 33 Heat Treatment of AISI 52100 Steel 37 iii

LIST OF ILLUSTRATIONS Table Page I. Calculated Residual Stresses and Their Depths Below the Surface 2 Figure 1. Probable stress distribution in hardened outer race. 3 2. Diameter change vst metal removed for hardened outer race. 5 3. Method of cutting bearing race. 32 4, Residual stress analysis for cut hardened outer race. 34 5, Outer bearing race. 36 V

i

ABSTRACT The failure of anti-friction bearing races usually results from fatigue induced by cyclical ball loads, Bearing life may be significantly increased if residual compressive stresses can be developed in surface regions which are normally subjected to tensile stresses in service, The results of this investigation indicate that average compressive residual stresses of the order of 30,000 to 40,000 psi may be developed initially in the first few thousandths of an inch beneath the outer surface of a heat-treated 52100 bearing race. When the race has been completely finished to size after hardening and tempering, those regions in which compressive residual stresses are developed by hardening have been removed, so that no beneficial residual stresses remain to influence and increase bearing life, vii

INTRODUCTION The failure of the balls and races of anti-fraction bearings is usually due to fatigue. The cyclical nature of the rotating loads and the development of Hertzian stresses ultimately lead to a spalling of either or both of the elements of the bearing. Under such conditions anything which can induce significant residual compressive stresses in the loaded surfaces and slightly below them may greatly improve the service life of a bearing. Two possibilities for developing favorable residual compressive stresses lie either in the hardening of the balls and races or in some machining operating such as grinding. In either case such residual stresses must lie far enough beneath the surface not to be removed when the balls or races are finished to size. They must lie in regions where tensile stresses develop under normal loading. In the particular case at hand, an investigation was made to determine the nature and magnitude of whatever stresses might be developed in the outside diameter of an outer race of a ball bearing as a result of hardening the race, 1I

I. SUMMARY AND INTERPRETATION OF RESULTS This report is divided into three major sections. Section I includes a summary and interpretation of the results of the investigation. Section II presents a detailed summary of the various test data and their correlation. Section III includes details of the setups and the procedures by which the data were taken and analyzed. The results of these- investigations lead to the conclusion that the hardening of 52100 steel outer bearing races induces residual compressive stresses in the outer layers. These compressive stresses may be on the order of perhaps as high as 50,000 psi maximum if a generalized analysis of data is made. Figure 1 shows a plot of what the distribution of such stresses might be. However, these stresses are only a few thousandths of an inch (0001-0.004 in.) below the surface, and these outer layers are removed by the subsequent grinding necessary to finish the outside diameters to the proper dimension. As a consequence, any beneficial residual stresses that might be developed by hardening are eliminated, and only residual stresses arising from the grinding operations remain. Table I is a compilation of the calculated residual stresses and their TABLE I CALCULATED RESIDUAL STRESSES AND THEIR DEPTHS BELOW THE SURFACE Group Metal Ground Off, Average Stress, No, O.D., In. Psi 1 0.00177 13,100 Tension 2 0.00462 38,000 Compr. 3 0.00723 21,800 Tension 4 0.00973 7,100 Tension 5 0,01223 2,180 Tension 6 0.01500 10,900 Compr. 7 0.00000 21,800 Tension depths from the hardened surface. These stresses have been calculated by treating one quarter of the bearing race as a simple cantilever and using the analysis shown in Fig. 4 of Section III. They should be considered as 2

40 /OUTER SURFACE 0 DISYANCE BELOW SURFACE -IN. I {y) ~ Fig. 1. Probable stress distribution in hardened outer race. ~ 20 I OI,\^_______^^ ^AVE RAGE MAXIMUM COMPRESS IVE STRESS — ~ ~-,APROBABLE MAXIMUM COMPRESSTVE ST,_SS Fig. I, Probable stress distribution in harcenec outer race.

average stresses based on the average change in diameter of fifteen specimens after an average of 0.001 in. of metal was ground from the outside diameter of each of six groups in one or more passes. In the case of Group 1, which had a nominal 0,001 in. ground off the outside diameter but did not clean up because its out-of-roundness was greater than 0.001 in., the calculated values are somewhat questionable and may be low. A plot of the change in outside diameter of the bearing race when cut versus the amount of metal removed from the outside diameter, as shown in Fig. 2, will give some idea of what the nature and levels of stress are in the layers removed by grinding. The nature or direction of the stress in a particular layer, whether tension or compression, can be determined by what effect its removal has upon the change in diameter of the race when the race has been cut after the layer has been removed. If the diameter were unchanged, then the layer would have had no stress in it. If the diameter increase is less than the diameter increase due to the removal of the prior layer, then the stress in the removed layer would be tensile. If the diameter increase is greater than the diameter increase due to the removal of the prior layer, then the stress in the removed layer is compressive. Thus, in the races considered, the layers between 0.002 and 0.003 in. and those between 0.005 and 0.006 in. are in compression, when results in an increase in the diameter when they are removed by grinding and their restraining influence is removed. Figure 1 is a plot of the probable stress distribution as a function of its depth beneath the surface of the hardened race. It represents more nearly the idealized situation that could be expected rather than what was actually determined. The failure of the races in Group 1 to clean up when initially ground and the subsequent effect on the change in diameter when the races was cut tended to shift the stress distribution to the right as shown by Fig. 2. In addition the effect of anytresidual stresses on the inside diameter as a result of heat treatment were neglected since the primary concern was a determination of stresses beneath the outer surface. Finally, so long as the general nature and magnitude of the stresses just beneath the outer surface had been established, it was deemed unnecessary to further refine their exact distribution. 4

H 3 0 ~ -.008 i r — SStatistical Analysis ) p^- -~oj —-Arithmetic Average o.006.004 w.0020 \ 0* 0.002.Od4.006.0 8. 0 0 01ol.01 METAL GROUND OFF OUTSIDE DIAMETER - IN. Fig. 2b Diameter change vs. metal removed for hardened outer race,

II. RESULTS OF DETAILED INSPECTION Tabulated on the following pages are the inspection data on the six groups, of fifteen outer races each, used to establish the diameter changes that resulted from hardening, grinding, and cutting, SPECIMEN NUMBERS ARRANGED BY INCREASING SIZE AND GRINDING GROUPS Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7 Spec. Spec. Spec. Spec. Spec. Spec. Spec. No. No. No. No. No. No. No. 29 17 68 85 50 78 36 114 18 81 38 48 28 70 31 96 26 118 25 77 45 97 99 80 61 13 104 57 33 30 94 10 86 11 59 117 55 115 119 111 106 34 2 41 32 101 79 23 20 54 116 22 1 40 95 14 73 92 4 75 82 12 8 47 5 64 91 112 6 103 88 93 42 56 49 44 108 35 120 19 51 52 63 110 3 39 105 37 66 21 46 72 43 69 102 71 53 87 9 24 62 58 65 7 84 Note: Group 1: 0.002 in. to be removed from the diameter in one step. Group 2: 0,004 in, to be removed from the diameter in two equal steps. Group 3: 0,006 in. to be removed from the diameter in three equal steps. Group 4: 0,008 in, to be removed from the diameter in four equal steps. Group 5: 0.010 in. to be removed from the diameter in five equal steps. Group 6: 0.012 in, to be removed from the diameter in six equal steps. Group 7: Unground; as received after hardening. 6

TEST GROUP DIAMETERS BEFORE GRINDING Average Diameter = 2.84825 in. Deviation of Deviation of Specimen Diameter, Sonofpecimen Diameter, De No. in. Diameter from Diameter from No. -in. No, in,.... Average Average 1 2,84835 + 10 41 2,84705 -120 2 2.84627 -198 142 2.84783 42 3 2.84655 -170 43 2, 84746 -79 4 2.84770 - 5 44 2.84982 +157 5 2.84731 - 94 45 2.85075 +250 6 2.84979 +154 46 2,85150 +325 7 2.84997 +172 47 2.84637 -193 8 2.85030 +205 48 2.84852 + 27 9 2.84672 -153 49 2.84897 + 72 10 2.84832 + 7 50 2.84852 + 27 11 2,84959 +134 51 2.84844 + 19 12 2.84979 +154 52 2.84901 + 76 13 2.84858 + 33 53 2.84992 +167 14 2.85076 +251 5-4 2.84628 -197 15 2. 85173 +348 55 2.84700 -125 16 2.84532 "293 56 2,84843 + 18 17 2.84675 -150 57 2.85078 +253 18 2.84675 -150 58 2.84850 + 25 19 2. 84786 -139 59 2.85150 +325 20 2.85016 +191 60 2.85197 +372 21 2.84984 +159 61 2.84830 + 5 22 2,84768 - 57 62 2.84808 - 17 23 2,84965 +140 63 2,84984 +159 24 2.84751 - 74 64 2.84773 + 52 25 2.84856 + 31 65 2,84904 + 77 26 2.84759 66 66 2.84903 + 76 27 2.84321 504 67 2. 85146 +321 28 2.84932 +107 68 2.84758 - 67 29 2,84566 -259 69 2.84804 21 30 2,84692 -133 70 2,85038 +213 31 2.84584 -141 71 2.84903 + 78 32 2.84764 - 61 72 2.84668 -157 33 2 84606 -219 73 2.84630 -195 34 2,85032 +207 74 2.84475 -350 35 2.84645 -180 75 2.84838 + 13 36 2 85062 +237 76 2,85190 +365 37 2.84844 + 19 77 2.84955 +130 38 2,84818 - 7 78 2,84922 + 97 39 2,84743 82 79 2. 84874 + 49 40 2.84884 + 59 80 2.84762 - 63 7

Concluded Deviation of Deviation of Specimen Diameter,er from Specimen Diameter, Diameter from Diameter from No. in. No. in. _in. Average No. in. Average 81 2.84759 - 66 101 2.84834 + 9 82 2.84896 + 71 102 2.84847 + 22 83 2.85259 +434 103 2.85057 +232 84 2 85109 +284 104 2.84958 +133 85 2.84812 - 13 105 2.84791 - 34 86 2.84863 + 38 106 2,84960 +135 87 2.85027 +202 107 2. 85010 +185 88 2.84641 -184 108 2.85025 +200 89 2.85082 +257 109 2.85350 +525 90 2.85393 +568 110 2.85012 +187 91 2,84839 + 14 111 2.84868 + 23 92 2.84713 -112 112 2.84897 + 72 93 2.84733 - 92 113 2.85175 +350 94 2,84763 - 62 114 2,84580 -245 95 2.84966 +141 115 2,84764 - 61 96 2.84687 -138 116 2.84709 -116 97 2,84591 -234 117 2.84624 -201 98 2,85293 +468 118 2,84822 - 3 99 2,84688 -137 119 2,84833 + 8 100 2.85351 +526 120 2,84735 - 90 8

MAXIMUM DIAMETER'MEASUREMENTS Specimen Maximum Diameter at 90~ to Difference No. Diameter Maximum Diameter x 10-5 Group 1 29 2.84566 2,84241 +325 114 2.84580 2.84545 + 35 31 2.84584 2.84493 + 91 97 2.84591 2.84599 - 8 33 2.84606 2,84287 +319 117 2,84624 2.84242 +382 2 2.84627. 84064 +563 54 2.84628 2.84298 +330 73 2.84630 2.84332 +298 47 2,84637 2.84352 +285 88 2,84641 284515 +126 35 2.84645 2.84383 +262 3 2.84655 2.84376 +279 72 2.84668 2.84167 +501 9 2,84672 2, 84632 + 40 Average 3828 Group 6 78 2.84922 2,84496 +426 28 2,84932 2.84%42 +390 77 2 84955 2.84342 +613 104 2.84958 2. 84415 +543 11 2.84959 2.84520 +439 106 2.84960 2.84762 +198 23 2.84965 2.84360 +605 95 2.84966 2.84430 +536 12 2.84979 2.84790 +189 6 2.84979 2.84584 +397 44 2,84982 2 84528 +454 63 2.84984 2.84439 +545 21 2.84984 2.84321 +663 53 2 84992 2.84282 +710 7 2,84997 2.84066 +931 Average 7637 9

AVERAGE DIAMETER MEASUREMENTS BEFORE AND AFTER GRINDING Average Diameter Average Diameter Specimen Before Grinding After Grinding Difference No. (in.) (in) x 10-5 in. Group 1 29 2.84566 2.84444 122 114 2.84580 2.84438 142 31 2.84584 2.84450 134 97 2.84591 2.84455 146 33 2.84606 2.84418 188 117 2.84624 2.84458 166 2 2.84627 2.84448 179 54 2.84628 2.84456 172 73 2.84630 2.84451 179 47 2.84637 2.84454 183 88 2.84641 2.84459 182 35 2.84645 2.84446 199 3 2.84655 2.84448 207 72 2.84668 2.84429 239 9 2.84672 2.84435 218 Average 2.84624 2.84447 177 Group 2 17 2.84675 2.84250 425 18 2.84675 2.84295 430 96 2.84687 2.84251 436 99 2.84688 2.85255 433 30 2.84692 2.84254 438 55 2.84700 2.84255 445 41 2.84705 2.84255 450 116 2.84709 2.84256 453 92 2.84713 2.84263 450 5 2.84731 2.84247 484 93 2.84733 2.84247 486 120 2.84735 2.84246 489 39 2.84743 2.84250 493 43 2.84746 2.84243 503 24 2.84751 2.84237 14 Average 2.84712 2. 84250 462 10

AVERAGE DIAMETER MEASUREMENTS BEFORE AND AFTER GRINDING Average Diameter Average Diameter Specimen Before Grindi Grindig Difference Before Grinding. Afte(Grinding x 10-5 in. No.-_(in.) (in.) X' Group 3 68 2.84758 2.84051 707 81 2.84759 2,84048 711 26 2.84759 2.84053 706 80 2.84762 2.84049 713 94 2.84763 2.84053 710 115 2.84764 2.84053 711 32 2.84764 2.840o 710 22 2.84768 2.84053 71 4 2.84770 2.84053 717 64 2.84773 2.84060 713 42 2.84783 2.84053 730 19 2.84786 2.84052 734 105 2.84791 2.84047 744 69 2.84804 2.84047 757 62 2.84808 2.84036 772 Average 2.84774 2.84051 723 Group 4 85 2.84812 2.83864 948 38 2.84818 2.83865 953 118 2.84822 2.83859 963 61 2.84830 2.83868 962 10 2.84832 2.83867 965 119 2.84833 2.83868 965 101 -2.84834 1 2.84835 2.83874 961 75 2.84838 2.83862 976 91 2.84839 2.83863 976 56 2.84843 2.83865 978 51 2.84844 2.83864 980 37 2.84844 2.83853 991 102 2.84847 2.83848 999 58 2.84850 2.83847 100 Average 2.84835 2.83862 973 II

AVERAGE DIAMETER MEASUREMENTS BEFORE AND AFTER GRINDING Average Diameter Average Diameter Specimen Before Grinding After Grinding Difference No. (in.) (in.) (x o5 in. Group 5 50 2.84852 2.83657 1195 48 2.84852 2.83659 1193 25 2.84856 2.83682 1174 13 2.84858 2.83659 1199 86 2.84863 2.83663 1200 111 2.84868 2.83660 1208 79 2.84874 2.83658 1216 40 2.84884 2.83654 1230 82 2.84896 2.83662 1234 112 22.84897 2.83663 1234 49 2.84897 2.83657 1240 52 2.84901 2.83649 1252 66 2.84903 2.83646 1257 71 2.84903 2.83641 1252 65 2.8490 2.283638 1266 Average 2.84881 2.83657 1223 Group 6 78 2.84922 2.83455 1467 28 2.84932 2.83461 1471 77 2.84955 2.83463 1492 104 2.84958 2.83463 1495 11 2.84959 2.83470 1489 106 2.84960 2.83475 1485 23 2.84965 2.83473 1492 95 2.84966 2.83474 1492 12 2.84979 2.83473 1506 6 2.84979 2.83473 1506 44 2.84982 2.83476 1506 63 2.84984 2.83473 1511 21 2.84984 2.83470 1514 53 2.84992 2.83471 1521 7 2. 84997 2. 83471 126 Average 2.84962 2. 83469 1500 12

AVERAGE DIAMETER MEASUREMENTS BEFORE AND AFTER CUTTING Specimen Average Diameter Average Diameter Difference Specimen Difference Nefo. meBefore Cutting After Cutting, / \(in.) -.(in.) Group 1 29 2.84444 2.84489 +45 114 2.84438 2.84405 -33 31 2.84450 2.84470 +20 97 2.84455 2.84484 +29 33 2.84418 2.84455 +37.117 2.84458 2.84517 +59 2 2.84448 2.84477 +29 54 2.84456 2.84459 +03 73 2.84451 2.84534 +83 47 2.84454 2.84521 +67 88 2.84459 2.84514 +55 35 2.84446 2.84438 -08 3 2.84448 2.84463 +15 72 2.84429 2.84433 +04 9 2.84454 2.84391 -63 Average 2.84447 2.84470 +23 Group 2 17 2.84250 2.84328 +78 18 2.84245 2.84316 +71 96 2.84251 2.84268 +17 99 2.84255 2.84332 +77 30 2.84254 2.84344 +90 55 2.84255 2.84350 +95 41 2.84255 2.84264 +09 116 2.84256 2.84337 +81 92 2.84263 2.84330 +67 5 2.84247 2.84330 +83 93 2.84247 2.84278 +31 120 2.84246 2.84355 +99 39 2.84250 2.84335 +85 43 2.84243 2.84326 +83 24 2.84237 2.84301 +64 Average 2.84250 2.84320 +69 13

AVERAGE DIAMETER MEASUREMENTS BEFORE AND AFTER CUTTING Specimen ^Average Diameter Average Diameter Difference Specimen Difference No^ ~ Before Cutting After Cutting - No. (in.).(in.) x 10-5 in. Group 3 68 2.84051 2.84091 +50 81 2.84048 2.84170 +122 26 2.84053 2.84059 +06 80 2.84049 2.84105 +56 94 2.84053 2.84076 +23 115 2.84053 2.84088 +35 32 2.84054 2.84109 +55 22 2.84053 2.84099 +46 4 2.84053 2.84121 -68 64 2.84060 2.84059 -01 42 2.84053 2.84087 +34 19 2.84052 2.84044 -08 105 2.84047 2.84110 +63 69 2.84047 2.84102 +55 62 2.84036 2.84023 -13 Average 2,84051 2.84090 +40 Group 4 85 2.83864 2.83897 +33 38 2.83865 2.83789 -76 118 2.83859 2.83868 +09 61 2.83868 2.83807 -61 10 2.83867 2.84004 +137 119 2.83868 2.83869 +01 101 1 2.83874 2.83861 -13 75 2.83862 2.83827 -35 91 2.83863 2.83829 -34 56 2.83865 2.83946 +81 51 2.83864 2.83887 +23 37 2.83853 2.83891 +38 102 2.83848 2.83870 +22 58 2.83847 2.83911 +64 Average 2.83862 2.83875 +13 14

AVERAGE DIAMETER MEASUREMENTS BEFORE AND AFTER CUTTING Specimen Average Diameter Average Diameter Difference Noc Before Cutting After Cutting D f ee No.' x 10-5 in. (in. ) (in.)..... Group 5 50 2.83657 2.83662 +05 48 2.83659 2.83607 -52 25 2.83682 2.83713 +31 13 2.83659 2.83729 +70 86 2.83663 2.83607 -56 111 2.83660 2*83710 +50 79 2.83658 2.83721 463 40 2.83654 2.83661 +07 82 2.83662 2.83621 -41 112 2.83663 2.83600 -63 49 2.83657 2.83604 -53 52 2.83649 2.83683 +34 66 2.83646 2.83579 -67 71 2.83641 2.83640 -01 63 2.83638 2.83651 +13 Average 2.83657 2.83653 -04 Group 6 78 2.83455 2.83518 +63 28 2.83461 2.83491 +30 77 2.83463 2.83471 +08 104 2.83463 2.83503 +40 11 2.83470 2.83467 -03 106 2.83475 2.83571 +96 23 2.83473 2.83478 +05 95 2.83474 2.83479 +05 12 2.83473 2.83522 +49 6 2.83473 2.83454 -19 44 2.83476 2.83483 +07 63 2.83473 2.83448 -25 21 2.83470 2.83436 -34 53 2.83471 2.83470 -01 7 2.83471 2.83532 +61 Average 2.83469 2.83488 +19 15

AVERAGE DIAMETER MEASUREMENTS BEFORE AND AFTER CUTTING Specimen Average Diameter Average Diameter Difference No. (Before Cutting After Cutin No'. x 10-5 in. (in.) (in.) Group 7 36 2.85062 2.85097 +35 70 2.85038 2.85018 -20 45 2.85075 2.85126 51 57 2.85078 2.85160 +82 59 2.85150 2.85145 -05 34 2.85032 2.85069 +37 20 2.85016 2.85038 +22 14 2.85076 2.85070 -06 8 2.85030 2.85132 +102 103 2.85057 2.85077 +20 108 2.85025 2.85072 +47 110 2.85012 2.85065 +53 46 2.85150 2.85177 +27 87 2.85027 2.85080 +53 84 2.85109 2.85233 +124 Average 2.85062 2.85104 +41 16

GROUP 1 MAXIMUM DIAMETER MEASUREMENTS ATER GRINDING Specimen 1st Read. 2nd Read. 3rd Read. Average Dispersion No. (in. ) (in.) (in. ) (in. ).00001 in. 29 2.84442 2.84445 2.84446 2.84444 04 114 2.84440 2.84438 2.84438 2.84438 02 31 2.84454 2.84449 2.84448 2.84450 o6 97 2.84455 2.84453 2.84457 2.84455 04 33 2.84415 2.84417 2.84423 2.84418 08 117 2.84455 2.84459 2.84465 2.84458 10 2 2.84450 2.84447 2,84446 2.84448 04 54 2,84458 2.84455 2.84455 2.84456 03 73 2.84450 2.84450 2.844054 2.844 2 1 04 47 2.84456 2.84452 2.84454 2.84454 04 88 2.84458 2.84460 2.84459 2.84459 02 35 2.84445 2.84446 2.84446 2.84446 01 3 2.84450 2.84445 2.84450 2.84448 05 72 2.84430 2.84428 2.84430 2.84429 02 9 2.84455 2.84453 2.84455 2.84454 02 17

GROUP 1 MAXIMUM DIAMETER MEASUREMEN AFTER GRINDING (Diameter at 90~ to Maximum Diameter) Specimen 1st Read. 2nd Read. 3rd Read. Average Dispersion No. (in.) (in.) (in. ) (in. ).00001 in. 29 2.84263 2.84264 2.84261 2.84263 03 114 2.84443 2.84442 2.84449 2.84445 07 31 2.84431 2.84433 2.84435 2.84433 04 97 2.84455 2.84454 2.84449 2.84453 06 33 2.84260 2.84335 2.84360 2.84352 25 117 2.84259 2.84273 2.84272 2.84268 14 2 2.84130 2.84135 2.84132 2.84132 05 54 2.84302 2.84305 2.84304 2.84304 03 73 2.84367 2.84363 2.84370 2.84366 07 47 2.84373 2.84374 2.84372 2.84373 02 88 2.84453 2.84452 2.84457 2.84454 05 35 2.84375 2.84375 2.84372 2.84374 03 3 2.84379 2.84374 2.84362 2.84371 17 72 2.84220 2.84223 2.84223 2.84222 03 9 2.84463 2.84465 2.84470 2.84466 07 18

GROUP 1 MAXIMUM DIAMETER MEASUREMENTS AETER CUTTING Specimen 1st Read. 2nd Read. 3rd Read. Average Dispersion No.. (in.) (in.) (in.) (in.).00001 in. 29 2.84490 2.84489 2.84488 2.84489 02 114 2.84403 2.84405 2.84406 2.84405 03 31 2.84468 2.84472 2.84470 2.84470 04 97 2.84487 2.84481 2.84484 2.84484 06 33 2.84457 2.84454 2.84455 2.84455 03 117 2.84514 2.84518 2.84518 2.84517 04 2 2.84477 2.84480 2.84475 2.84477 05 54 22.84460 2.84462 2.84456 2.84459 06 73 2.84531 2.84536 2.84535 2.84534 05 47 2.84519 2.84524 2.84520 2.84521 05 88 2.84512 2.84516 2.84513 2.84514 04 35 2.84442 2.84437 2.84435 2.84438 07 3 2.84461 2.84464 2.84463 2.84463 03 72 2.84433 2.84432 2.84435 2.84433 03 9 2.84392 2.84392 2.84390 2.84391 02 19

GROUP 2 MAXIMUM DIAMETER MEASUREMENTS AFTER GRINDING Specimen 1st Read. 2nd Read. 3rd Read. Average Dispersion No. (in.) (in.) (in.) (in.).00001 in. 17 2.84244 2.84251 2.84254 2.84250 10 18 2,84243 2, 84245 2,84245 2,84245 02 96 2,84248 2,84250 2.84254 2 84251 06 99 2.84253 2.84255 2,84257 2.85255 04 30 2,84252 2.84254 2,84256 2,84254 04 55 2.84255 2.84256 2.84255 2.84255 01 41 2.84255 2.84255 2.84257 2.84255 02 116 2 84252 2 84257 2,84258 2.84256 06 92 2.84260 2.84263 2.84265 2.84263 05 5 2.84244 2.84249 2,84248 2.84247 05 93 2.84243 2.84250 2.84247 2.84247 07 120 2.84246 2.84246 2,84247 2.84246 01 39 2.84250 2.84251 2.84250 2.84250 01 43 2.84240 2.84244 2,84244 2.84243 04 24 2.84235 2.84240 2.84236 2.84237 05 20

GROUP 2 MAXIMUM DIAMETER MEASS AER CUTTING Specimen 1st Read. 2nd Read. 3rd Read. Average Dispersion No. (in.) (in.) - (in.) (in.).00001 in. 17 2.84328 2.84327 2.84328 2.84328 01 18 2,84315 2.84316 2.84317 2.84316 02 96 2.84268 2.84267 2.84269 2,84268 02 99 2.84330 2.84333 2.84332 2.84332 03 30 2.84343 2.84347 2.84343 2.84344 04 55 2.84349 2.84350 2.84350 2.84350 01 41 2.84264 2.84265 2.84264 2. 84264 01 116 2.84338 2.84337 2.84336 2.84337 02 92 2.84328 2.84330 2.84332 2.84330 04 5 2.84300 2.84300 2.84300 2.84300 00 93 2.84277 2.84278 2.84280 2.84278 03 120 2.84357 2.84354 2.84353 2 84355 04 39 2.84337 2.84335 2.84335 2.84335 02 43 2.84324 2.84326 2.84327 2.84326 03 24 2.84300 2.84301 2.84302 2.84301 02 21

G-ROUP 3 MAXIMUM DIAMETER NEASUREN0T2S AER GR INDING Specimen lst Read. 2nd Read. 3rd Read. Average Dispersion No. (in.) (in.) (in.) (in.).00001 in. 68 2.84050 2.84053 2.84050 2.84051 03 81 2.84047 2.84048 2.84048 2.840o8 01 26 2.84050 2.84055 2.8405+ 2.84053 05 80 2.84048 2,84049 2,84049 2.84049 01 94 2.84054 2.84053 2.84053 2.84053 01 115 2.84053 2.84055 2.84052 2.84053 03 32 2,84o03 2.84055 2.845 2.8405 02 22 2.84053 2.84052 2.84054 2.84053 02 4 2,84053 2.84053 2.84053 2.84053 00 64 2.84060 2.84060 2.84060 2.84060 00 42 2.8405 2.84053 2.84051 2.84053 03 19 2.84052 2.84052 2.84052 2.84052 00 105 2.84047 2.84048 2.84046 2.84047 02 69 2.84048 2.84047 2.84047 2.84047 01 62 2.84037 2.84035 2.84035 2.84036 02 22

GROUP 3 MAXUM DIAMER MEASUREMENTS AFFER CUTTING Specimen 1st Read. 2nd Read. 3rd Read. Average Dispersion No. (in.) (in.) (in.) (in.).00001 in. 68 2.84091 2.84092 2.84090 2.84091 02 81 2.84170 2.84172 2.84169 2.84170 03 26 2.84056 2.84060 2.84060 2,84059 04 80 2.84104 2.84105 2.84105 2,84105 01 94 2,84076 2.84077 2.84079 2.84076 03 115 2.84089 2.84088 2.84086 2.84088 03 32 2.84110 2,84110 2,84108 2.84109 02 22 2.84100 2.84098 2.84099 2.84099 02 4 2, 842. 2,84121 2 84121 2.84121 00 64 2.84058 2.84060 2.84060 2.84059 02 42 2.84087 2.84088 2.84087 2.84087 01 19 2.84042 2.84045 2.84045 2.84044 03 105 2.84110 2.84112 2.84108 2.84110 04 69 2.84102 2.84102 2,84101 2.84102 01 62 2,84019 2.84024 2,84027 2.84023 08 23

GROUP 4 MAXIMUM DIAMETER MEASUREMENTS AFTER GRINDING Specimen 1st Read. 2nd Read. 3rd Read. Average Dispersion No. (in.) (in.) (in.) (in.).00001 in. 85 2.83867 2.83862 2.83863 2.83864 05 38 2.83867 2.83865 2.83862 2.83865 05 118 2.83861 2.83858 2.83859 2.83859 03 61 2.83872 2.83866 2.83867 2.83868 06 10 2.83868 2.83867 2.83866 2.83867 02 119 2.83870 2.83868 2.83866 2.83868 04 101 See Note Below 1 2.83875 2.83875 2.83871 2.83874 04 75 2.83863 2.83862 2.83860 2.83862 03 91 2.83864 2.93963 2.83862 2.83863 02 56 2.83867 2.83865 2.83865 2.83865 02 51 2.83866 2.83864 2.83862 2.83864 04 37 2.83855 2.83852 2.83852 2.83853 03 102 2.83850 2.83847 2.83847 2.83848 03 58 2.83848 2.83847 2.83847 2.83847 01 107 2.83867 2.83865 2.83864 2.83865 03 Note: Specimen No. 101 not found in this group as listed in letter July 22, 1965. Specimen No. 107 in group instead. 24

GROUP 4 MAXIMUM DIAMETER MEASUENTS ATER CUTTING Specimen lst Read. 2nd Read. 3rd Read. Average Dispersion No. (in.) (in. ) (in.) (in. ).00001 in. 85 2.83898 2.83897 2.83896 2.83897 02 38 2.83787 2.83790 2.83789 2.83789 03 118 2.83867 2.83868 2.83868 2.83868 01 61 2.83805 2.83808 2.83807 2.83807 03 10 2.84003 2.84005 2.84005 2.84004 02 119 2.83875 2.83865 2.83866 2.83869 10 107 2.83882 2.83878 2.83878 2.83879 04 1 2.83860 2.83862 2.83862 2.83861 02 75 2.83827 2.83827 2.83826 2.83827 01 91 2.83829 2.83830 2.83829 2.83829 01 56 2.83944 2.83950 2.83944 2.83946 06 51 2.83884 2.83886 2.83890 2.83887 06 37 2.83890 2.83892 2.83890 2.83891 02 102 2.83869 2.83871 2.3870 2.83870 02 58 2.83912 2.83911 2.83911 2.83911 01 25

GROUP 5 MAXIMUM DIAMETER MEASURENTS AFTER GRINDING Specimen 1st Read. 2nd Read. 3rd Read. Average Dispersion No. ( in.) (in.) (in.) (in.).00001 in. 50 2.83660 2.83656 2.83655 2.83657 05 48 2.83660 2.83659 2.83657 2.83659 03 25 2.83685 2.83680 2,83682 2.83682 05 13 2.83662 2.83658 2.83658 2.83659 04 86 2.83665 2.83662 2.83663 2.83663 03 111 2.83660 2.83660 2.83661 2.83660 01 79 2.83661 2.83658 2.83657 2.83658 04 40 2.83655 2.83653 2.83653 2.83654 02 82 2.83662 2.83662 2.83662 2.83662 00 112 2.83663 2.83665 2.83660 2.83663 05 49 2.83657 2.83656 2.83658 2.83657 02 52 2.83652 2.83648 2.83647 2.83649 05 66 2.83648 2.83645 2.83645 2.83646 03 71 2.83642 2.83640 2.83640 2.83641 02 65 2,83639 2.83637 2.83637 2.83638 02 26

GROUP 5 MAXIMUM DIAMETER MEASUPEMBTTS AFTER CUTTING Specimen 1st Read. 2nd Read. 3rd Read. Average Dispersion No. (in.) (in.) (in.) (in.).00001 in. 50 2.83663 2.83662 2.83660 2.83662 03 48 2.83607 2.83608 2.83606 2.83607 02 25 2.83705 2.83718 2.83716 2.83713 13 13 2.83728 2.83729 2.83730 2.83729 02 86 2.83607 2.83607 2.83608 2.83607 01 111 2.83710 2.83709 2.83710 2.83710 01 79 2.83723 2.83720 2.83720 2.83721 03 40 2.83662 2.83661 2.83660 2.83661 02 82 2.83621 2.83621 2.83622 2.83621 01 112 2.83600 2.83600 2.83600 2.83600 00 49 2.83603 2.83602 2.83606 2.83604 04 52 2.83683 P283684 2.83683 2.83683 01 66 2.83580 2.83579 2.83579 2.83579 01 71 2.83639 2.83640 2.83640 2.83640 01 65 2.83652 2.83651 2.83651 2.83651 01 27

GROUP 6 MAXIMUM DIAMETER MEASUREMETS AFTER GRINDING Specimen lst Read 2nd Read 3rd Read Average Dispersion No. (in.) (in.) (in..) (in.).00001 in. 78 2.83457 2.83452 2.83457 2.83455 05 28 2.83463 2.83463 2.83458 2.83461 0 77 2.83465 2.83463 2,83462 2.83463 03 104 2.83465 2.83463 2.83464 2.83463 02 11 2.83470 2.83470 2.83469 2.83470 01 106 2.83477 2.83474 2.83474 2.83475 03 23 2.83475 2.83472 2.83471 2.83473 04 95 2.83476 2.83473 2.83474 2.83474 03 12 2.83475 2.83472 2.83472 2.83473 03 6 2.83475 2.83471 2.83473 2.83473 04 44 2.83478 2.83478 2.83472 2.83476 06 63 2.83474 2.83472 2.83473 2.83473 02 21 2.83472 2.83467 2.83470 2.83470 05 53 2.83473 2.83471 2.83469 2.83471 04 7 2.83473 2.83470 2.83470 2.83471 03 28

GROUP 6 MAXIMUM DIAMETER MEASUREMENTS AFTER GRINDING (Dia. at 90~ To Max. Dia.) Specimen 1st Read. 2nd Read. 3rd Read. Average Dispersion No. (in.) (in.)_ (in.) (in.).00001 in. 78 2.83453 2.83451 2.83453 2.83452 02 28 2*83455 2.83456 2.83458 2.83456 03 77 2.83455 2.83458 2.83461 2.83458 06 104 2.83464 2.83464 2.83464 2.83464 00 11 2.83465 2*83465 2.83471 2.83467 06 106 2.83473 2.83472 2.83476 2.83474 05 23 2.83475 2.83475 2.83473 2.83474 02 95 2.83469 2.83470 2.83470 2.83470 01 12 2.83470 2.83470 2.83475 2.83472 05 6 2.83473 2.83475 2.83476 2.83475 03 44 2.83471 2.83477 2.83473 2.83474 06 63 2,83472 2.83472 2.83472 2.83472 00 21 2.83468 2.83469 2.83469 2.83469 01 53 2.83465 2.83468 2.83470 2.83468 05 7 2.83472 2.83470 2.83468 2.83470 04 29

GROUP 6 MAXMUM DIAMETER MEASUREMENTS AFTER CUTTING Specimen lst Read. 2nd Read. 3rd Read. Average Dispersion No. (in.) (in.) (in.) (in.).00001 in. 78 2.83518 2,83520 2.83516 2.83518 04 28 2.83493 2*83491 2.83489 2.83491 04 77 2.83472 2,83,72 28370 283471 02 104 2*83503 2.83503 2.83502 2.83503 o0 11 2.83470 2.83467 2.83465 2.83467 05 106 2.83572 2.83571 2.83571 2.83571 01 23 2.83478 2.83478 2.83477 2.83478 01 95 2.83480 2.83478 2.83478 2.83479 02 12 2.83523 2.83522 2.83522 2.83522 01 6 2.83455 2.83454 2.83453 2.83454 02 44 2.83484 2.83482 2.83482 2.83483 02 63 2.83446 2.83449 2.83448 2.83448 03 21 2.83437 2.83434 2.83436 2.83436 03 53 2.83471 2.83469 2.83470 2.83470 02 7 2.83532 2.83532 2.83532 2.83532 00 30

III. ANALYTICAL PROCEDURES If residual stresses are present in hardened bearing races as a result of hardening treatments, then, since such stresses are elastic, reducing those stresses to zero should result in a corresponding strain from which the nature and magnitude of the residual stresses can be calculated. The problem, then, is to determine the strain when hardened races relax elas — tically. Therefore, the approach used was to measure accurately the outside diameters of bearing races before and after removing a predetermined amount and then to measure the diameter change after cutting the race, as shown in Fig. 3, and allowing it to relax. This approach enables the principal stress, that tangent to the bearing, to be calculated in the manner of a cantilever beam and ignores the small stresses in the other two directions. There was considerable variation in the outside diameter of an initial sample of 20 bearings, which was inspected and centerless ground in groups of five each to remove nothing, 0.002 in., 0,004 in., and 0o006 in. from the outside diameter after hardening. Because of such variations, it was decided that a larger sample must be used and that the races must be as close to the same size as possible and uniformly subjected to essentially the same processes. As a result a group of 110 bearings, hardened but unground, were inspected and grouped into lots of 15 each with a minimum size variation within each group, Group 1 was centerless ground to remove nominally 0.002 in. from the outside diameter in one pass. Group 2 was centerless ground to remove 0.002 in. from the outside diameter in two equal passes, Group 3 was centerless ground to remove 0.006 in. from the outside diameter in three equal passes. Group 4 was ground to remove 0.008 in. in four equal passes, Group 5 was ground to remove 0.010 in. in five equal passes. Group 6 was ground to remove 0.012 in. in six equal passes, Group 7 had nothing done to it and represented the as-hardened condition. After the grinding, the bearing diameters were again measured at the same point, after which they were cut at right angles to the measured diametero An abrasive cut-off machine was used, with an emulsion as coolant. The diameter at right angles to the cut was again measured to determine the elastic strain that resulted from the release of the residual stresses. MEASURING TECHNIQUES The outside diameter of the bearing race was measured by use of a Sheffield Comparator, Style 5000, Serial No. 1068RS, with a least reading of 25 millionths of an in, (0.000025 in,). It was set to the appropriate dimension by use of gage blocks, Johansson Standard Set I-A, Serial No, 42530 31

CUT HERE L' r- R NEUTRAL ///~ MEASURED DIA. z \MATER#L REMOVED BY GRINDING, AR DISTANCE TO NEUTRAL AXIS, C QUARTER SEC TION. FOR STRESS EVALUATI ON Fig. 3. Method of cutting bearing race. The outer race has been ground on the outside diameter, with an amount AR removed. It is then cut at right angles to the measured dia. and measured again. The stress is computed by treating one quarter of the race as a simple cantilever beam for which one half the change in diameter becomes the deflection as a result of the internal stresses. For the exact analytical relations, see the rest of the report. 32

Each race was measured to determine its maximum diameter, which was then marked and used for future measurements. Each race was measured three times by the same person under essentially the same conditions. The average of the three readings was used as the diameter. A statistical analysis of the measurement data was made to verify the validity of using the arithmetic average as the representative diameter. The originally measured diameters followed a Gaussian distribution, but this was eliminated when they were grouped into more nearly uniform sized lots of fifteen each. This changed the distribution to a modified log-normal type, which permitted the use of a Weibull distribution since one could assume that the sample size was homogeneous and that identical treatments had been given to each specimen within a group. A Weibull distribution follows the general equation f(x) = b ( b- e which can be modified to give a straight line when plotted on Weibull graph paper with diameter size and frequency of occurrence used as coordinates. After the data were plotted, the 50% readings were taken as the statistical mean. In every case the difference between the statistical mean and the arithmetic average was insignificant, which justifies the use of the arithinetic average as the measured diameter. STRESS CALCULATIONS Figure 4 shows the analysis of the stress in the outer part of the races as a result of the relaxation due to cutting the race. One quarter of the race is treated as a simply supported cantilever beam which has deflected an amount, y', equal to half the change in diameter of the cut race. Practically, the average change in diameter or deflection of each group can be ascribed to the removal of a stressed layer of metal 0.001 in. thick by each grinding operation. Thus: b y = s- - X- dx a E= IR2E de EI = 3 33

Pas;~/~~~v4 APPRXc^rdS f4K Cux-oyf N~JAD/O,S07 ar Aks/.a 8aAAd /cc Sp6CAE7l/.To1P C WCoW FGoA~T Vw' Fig.we 4lsre POSny r/ou' /A /6 & te r Fig. 4. Residual stress analysis for cut hardened outer race.

MR2 2 MR e EI 2 M2 2 EI 8 where M = bending moment X = Re dx = Rde e = t/2 radians E = modulus of elasticity I = moment of inertia For the particular situation shown in Fig. 4 (see also Fig. 5), M = a. w AR c where a stress, unknown w = width across which a acts, 0.68 in. AR = thickness of material removed in grinding, on which a acts c = distance from neutral axis to outer fiber, 0*10 in. Substituting in the equation above gives 22 Y'= -E x a w AR c 8EI ^ a= 8EIy'.t2R2W AR c For the race used, E = 30 x 106, and 3 I 2 where t = c. 8 wts, y" cr E.. 4Et y' 32R2I R 12

0.68 ______ - _____N.A. CD 4 0 c0I CM 1 Fig.5 Outer bearing race. 207 Size Outer Race, Conrad Type AISI 52100 Steel, Vacuum Deoxidized Nominal Finished Outside Diameter, 2.830 In. Nominal Inside Diameter, 2.515 In. 36

~-, 4 x 30 x 106 (.2)y'... n = 352( 1.22)2(.001) =10,9 107 Yn where R = 1.22 in. t = 0.2 in. w =.68 in. AR = 0.001 in. ~. For: Group 1, y' = + 1.2 x 10-4 in.; a1 = 10.9 x 1.2x 104 x 107 = 13,100 psi o_4 -4 Group 2, y' = + 2.0 x 104 in.; a2 = 109 x 3.5x 107 x10 ~2 = 38.9 x ~.5'x~ pS7' 38,000 psi -4 - 7 Group 3, y' = + 2.0 x 10 in.; a3 10.9 x 2.0' xl0-4 x 10 = 21,800 psi -4 4 7., Group 4, y' = + 0.65 x 10 in,; a4 = 10.9 x.6'x 10 x = 7,100 psi Group 5, y' = - 0.2 x 10 in.; a5 = 10.9 x 0. x 10 x 107 = 2,180 psi -4 -4. 7' Group 6, y' = +1.0 x 10 in.; a6 = 10.9 x 1.0x 0 x 1 10 = 10,900 psi Group 7, y' = + 2.0 x 10-4 in.; a7 = 10.9 x 2.0 x 10-4 x 107 = 21,800 psi These calculated stress values represent only the average for an average increment of 0.001 in. metal removal. Actual differences in the parameters, as opposed to the nominal values used, may result in stresses perhaps 50% or more above the calculated values. HEAT TREATMENT OF AISI 52100 STEEL Procedure used at Bearings Corporation of America: 1. Heat at 1540~F + 50F for 30 to 40 minutes at heat with a dewpoint of 30-35 F for the endothermic atmosphere in the furnace. 37

2. Oil quench in oil of 130~-1500F. 3+ Check for hardness; must be Rc 64-66 as quenched. 4. Wash parts. 5. Temper for 2 to 3 hours at 375~F ~ 50F. 6. Final hardness to be Rc 60-64, Grain size should be no larger than 8. 38

IIII1IIIilINIUMI 3901502841 2206