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<title>Probabilistic Peak: Why a Cut Passes Most of the Time and Occasionally Cracks the Cutter | HiAPI-C# 2025 </title>
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<h1 id="probabilistic-peak-why-a-cut-passes-most-of-the-time-and-occasionally-cracks-the-cutter">Probabilistic Peak: Why a Cut Passes Most of the Time and Occasionally Cracks the Cutter</h1>
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<p><img src="probabilistic-peak-crack-img/dartboard-engagement.png" alt="Spindle-moment dartboard and the matching 3D engagement for one spindle revolution">
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<em>Left — spindle-moment dartboard. The <code>(Mx, My)</code> moment-vector tip is drawn as a closed
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locus over one spindle revolution, coloured by the axial moment <code>Mz</code>; the concentric rings
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are moment magnitude (Nm). For most of the revolution the locus stays near the centre —
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small flute–workpiece contact length, small moment. One narrow lobe stretches out to the
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outer rings: the angle where the contact length spikes and produces the large force that
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can crack the flute. Right — the 3D engagement at that high-load phase, showing the flute
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deeply engaged with the workpiece.</em></p>
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<h2 id="the-mechanism">The Mechanism</h2>
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<p>The flute–workpiece contact length is small for most spindle angles and spikes only inside
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one <strong>narrow angular window</strong>. The large force — and the crack risk — exists only inside
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that window.</p>
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<p>The cutter's flutes are <strong>discrete</strong>. Whether a cutting flute actually lands inside the
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narrow high-contact window is a matter of flute phase, not a certainty:</p>
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<ul>
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<li><strong>High probability</strong> — the flutes fall in the wide low-contact region and step over the
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window. The pass completes safely.</li>
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<li><strong>Low probability</strong> — a flute lands inside the narrow window, takes the full contact
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length, and sees the large force. The flute can crack.</li>
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</ul>
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<p>This is why a cut with a clear high-contact window still passes most of the time and only
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occasionally breaks the cutter, and why nominally identical geometry can pass on one pass
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and crack on another. It is the same effect documented under
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<a href="cam-floating-point-drift.html#probabilistic-peak-dodging">Probabilistic Peak Dodging</a>.</p>
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<h2 id="see-also">See Also</h2>
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<ul>
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<li><a href="cam-floating-point-drift.html">CAM Floating-Point Drift</a> — a concrete case of the same
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probabilistic peak effect, triggered by sub-micron floor contact.</li>
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</ul>
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