Modeling of Self-Vibratory Drilling Head-Spindle System for Predictions of Bearings Lifespan

<table>(a) Components (SVDH-body, SVDH vibrating subsystem) and interfaces (spring and ball retainer), (b) identification of the stiffness: <svg height="10.7375" id="M67" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.7375)">
<g transform="translate(72,-63.41)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑘</tspan>
</text>
</g>
</g>
</svg> and the damping factor: <svg height="7.1875" id="M68" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 7.3874998 7.1875" width="7.3874998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1875)">
<g transform="translate(72,-66.25)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑐</tspan>
</text>
</g>
</g>
</svg> by minimizing the gap between <svg height="14.925" id="M69" style="vertical-align:-3.22281pt" version="1.1" viewbox="0 0 96.125 14.925" width="96.125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.925)">
<g transform="translate(72,-60.06)">
<text transform="matrix(1,0,0,-1,-71.95,63.32)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐀</tspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">𝐁</tspan>
</text>
<text transform="matrix(1,0,0,-1,-54.58,60.2)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝟏</tspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">𝟏</tspan>
</text>
<text transform="matrix(1,0,0,-1,-45.83,60.2)">
<tspan style="font-size: 8.75px; " x="0" y="0">-</tspan>
<tspan style="font-size: 8.75px; " x="2.9144161" y="0">r</tspan>
<tspan style="font-size: 8.75px; " x="5.8113279" y="0">e</tspan>
<tspan style="font-size: 8.75px; " x="9.697216" y="0">c</tspan>
<tspan style="font-size: 8.75px; " x="13.583104" y="0">o</tspan>
<tspan style="font-size: 8.75px; " x="17.959105" y="0">n</tspan>
<tspan style="font-size: 8.75px; " x="22.335104" y="0">s</tspan>
<tspan style="font-size: 8.75px; " x="25.669617" y="0">t</tspan>
<tspan style="font-size: 8.75px; " x="28.102673" y="0">r</tspan>
<tspan style="font-size: 8.75px; " x="31.218384" y="0">u</tspan>
<tspan style="font-size: 8.75px; " x="35.594383" y="0">c</tspan>
<tspan style="font-size: 8.75px; " x="39.48027" y="0">t</tspan>
<tspan style="font-size: 8.75px; " x="41.913326" y="0">e</tspan>
<tspan style="font-size: 8.75px; " x="45.799217" y="0">d</tspan>
</text>
</g>
</g>
</svg> and <svg height="14.925" id="M70" style="vertical-align:-3.22281pt" version="1.1" viewbox="0 0 61.924999 14.925" width="61.924999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.925)">
<g transform="translate(72,-60.06)">
<text transform="matrix(1,0,0,-1,-71.95,63.32)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐀</tspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">𝐁</tspan>
</text>
<text transform="matrix(1,0,0,-1,-54.58,60.2)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝟏</tspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">𝟏</tspan>
</text>
<text transform="matrix(1,0,0,-1,-45.83,60.2)">
<tspan style="font-size: 8.75px; " x="0" y="0">-</tspan>
<tspan style="font-size: 8.75px; " x="2.9144161" y="0">d</tspan>
<tspan style="font-size: 8.75px; " x="7.2904158" y="0">i</tspan>
<tspan style="font-size: 8.75px; " x="9.7234716" y="0">r</tspan>
<tspan style="font-size: 8.75px; " x="12.620384" y="0">e</tspan>
<tspan style="font-size: 8.75px; " x="16.506271" y="0">c</tspan>
<tspan style="font-size: 8.75px; " x="20.39216" y="0">t</tspan>
</text>
</g>
</g>
</svg>.</table>

Advances in Acoustics and Vibration

fig5

Figure 5

Figure 5: Modeling of Self-Vibratory Drilling Head-Spindle System for Predictions of Bearings Lifespan 