Free Keyway Broaching Cutting Force & Tonnage Tool

1. Broaching Mechanics & Specific Cutting Force ($k_c$)

Broaching is a high-productivity single-stroke machining process where each progressive tooth rises higher than the preceding tooth by an increment called Rise Per Tooth (RPT) or chip load. The cutting force per tooth is given by: $$F_{tooth} = w cdot RPT cdot k_c$$ Where $w$ is the keyway slot width, $RPT$ is the feed per tooth, and $k_c$ is the specific cutting force of the material ($1,800 ext{ MPa}$ for mild steel up to $2,600 ext{ MPa}$ for austenitic stainless).

2. Simultaneous Teeth in Cut ($Z_c$) & Stability Limits

The total cutting force experienced by the arbor press or hydraulic cylinder is the sum of all teeth cutting at the same instant: $$Z_c = ext{ceil}left(rac{L_{hub}}{P_{pitch}} ight)$$ $$F_{total} = Z_c cdot F_{tooth} cdot K_{dull}$$ Where $K_{dull} approx 1.25$ accounts for progressive edge dulling.

• Minimum Contact Rule ($Z_c ge 2$): At least two teeth must be engaged in the bore at all times. If $L_{hub} < 2 cdot P$, the broach will chatter, tilt sideways, and snap teeth off. If a hub is thin, stack multiple parts in a fixture.
• Maximum Contact Rule ($Z_c le 5$): Having too many teeth in cut simultaneously multiplies tonnage exponentially and risks buckling the push broach column.

3. Gullet Chip Capacity & Packing

Unlike milling or turning, chips cannot escape during the stroke; they must coil tightly inside the tooth gullet until the tooth clears the bottom of the bore. The curled chip volume expands by a factor of 3 to 4 compared to solid metal. If the gullet fill ratio exceeds $70%$, chips jam tightly against the work surface, causing galling, catastrophic broach breakage, and scored keyways.