Internal Loading Distribution in Statically Loaded Ball Bearings Subjected to an Eccentric Thrust Load

<table>Distance between loci of inner and outer raceway groove curvature centers for the maximum loaded ball, <svg height="16.625" id="M431" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 56.962502 16.625" width="56.962502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><path d="M352 391q0 -31 -27 -44q-14 -7 -24 6q-39 48 -84 48q-23 0 -39.5 -15t-16.5 -40q0 -43 73 -90q49 -32 70 -58t21 -57q0 -58 -62 -105.5t-129 -47.5q-40 0 -75.5 25t-35.5 52q0 28 32 46q7 4 15 3t11 -6q19 -31 48.5 -50.5t54.5 -19.5q34 0 54 19.5t20 42.5q0 43 -65 81
q-97 56 -97 123q0 50 51 96q19 17 58 32.5t62 15.5q37 0 61 -18t24 -39z" id="x1D460"></path></g><g transform="matrix(.017,-0,0,-.017,6.437,12.138)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,-0,0,-.017,12.319,12.138)"><path d="M642 419q-50 -36 -71 -94q-28 -78 -68 -170q-39 -89 -114 -135q-34 -21 -83 -31l-45 -219l-31 -31q-8 7 -15 29.5t-2 45.5l35 172q-153 10 -153 169q0 28 6 84q7 68 7 88q0 48 -27 48q-18 0 -51 -28l-7 26q62 75 118 75q49 0 49 -90q0 -47 -5 -81q-10 -72 -10 -108
q0 -117 82 -133l87 455l62 19l7 -2l-99 -478q91 12 131 120q34 93 51 154q20 73 36 88q42 40 103 56z" id="x1D713"></path></g><g transform="matrix(.017,-0,0,-.017,28.144,12.138)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,42.848,12.138)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,51.008,12.138)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g>
</svg>, as a function of lever arm, <svg height="7.9499998" id="M432" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 7.1624999 7.9499998" width="7.1624999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M391 364q0 -28 -20.5 -53.5t-50 -43.5t-70 -34t-73.5 -25t-68 -17v-29q0 -48 20 -81t65 -33q73 0 157 76l16 -23q-107 -113 -221 -113q-21 0 -40.5 6.5t-39 22t-31.5 47t-12 75.5q0 69 33.5 139.5t95.5 114.5q77 55 143 55q42 0 69 -24.5t27 -59.5zM313 350
q0 26 -14.5 40.5t-37.5 14.5q-32 0 -44 -7q-82 -46 -104 -175q200 49 200 127z" id="x1D452"></path></g>
</svg>.</table>

Mathematical Problems in Engineering

fig31

Figure 31

Figure 31: Internal Loading Distribution in Statically Loaded Ball Bearings Subjected to an Eccentric Thrust Load 