On the Boundary between Nonlinear Jump Phenomenon and Linear Response of Hypoid Gear Dynamics

<table>Illustration of different tooth impact types. No impact (<svg height="14.2375" id="M120" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 19.512501 14.2375" width="19.512501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑁</tspan>
</text>
<text transform="matrix(1,0,0,-1,-61.31,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
</g>
</g>
</svg>, <svg height="14.2375" id="M121" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 19.512501 14.2375" width="19.512501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑁</tspan>
</text>
<text transform="matrix(1,0,0,-1,-61.31,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
</g>
</g>
</svg>, and <svg height="14.3875" id="M122" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 19.512501 14.3875" width="19.512501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.3875)">
<g transform="translate(72,-60.49)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑁</tspan>
</text>
<text transform="matrix(1,0,0,-1,-61.31,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">3</tspan>
</text>
</g>
</g>
</svg>), single-sided impact (<svg height="14.475" id="M123" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 16.375 14.475" width="16.375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.475)">
<g transform="translate(72,-60.42)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑆</tspan>
</text>
<text transform="matrix(1,0,0,-1,-63.82,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
</g>
</g>
</svg>, <svg height="14.475" id="M124" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 16.375 14.475" width="16.375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.475)">
<g transform="translate(72,-60.42)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑆</tspan>
</text>
<text transform="matrix(1,0,0,-1,-63.82,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
</g>
</g>
</svg>), and double-sided impact (<i>D</i>).</table>

Advances in Acoustics and Vibration

fig6

Figure 6

Figure 6: On the Boundary between Nonlinear Jump Phenomenon and Linear Response of Hypoid Gear Dynamics 