§1One stroke, one shape
Broaching does in a single linear pass what other methods build up over many cuts: a broach carries the entire profile as a series of stepped teeth and imprints it as it travels through or across the work.
The idea is a staircase of cutting edges (the hero). The first teeth are smallest and each successive tooth stands a little taller, so as the broach passes, each tooth removes one thin layer and the last teeth leave the finished size and form. Because the whole profile is built into the tool, a single stroke produces a complete, accurate shape — an internal keyway, a square or hexagonal hole, a spline, or an external flat or form — with no indexing and no tool path. That makes broaching extraordinarily fast and repeatable, at the cost of a tool made for one shape only and a machine stiff and powerful enough to drive it. The rest of the page is about the two numbers that govern it: the rise per tooth and the pitch.
Contents§2Rise per tooth
The step by which each tooth is taller than the last — the rise per tooth — sets how much metal each edge removes and therefore how many teeth the broach needs to reach full depth.
The rise per tooth is the chip thickness each edge takes, typically a few hundredths of a millimetre. To broach a keyway 5 mm deep at a rise per tooth of 0.05 mm needs 5 ÷ 0.05 = 100 cutting teeth to reach depth. A finer rise gives a better finish and lighter cut but a longer broach; a coarser rise shortens the tool but loads each tooth more and roughens the surface. This is why a broach is long — the depth to be removed, divided by the small bite each tooth can safely take, dictates a great many teeth in a row, and the tool’s length follows directly from the depth of form it must cut.
§3Tooth pitch and teeth in cut
The spacing between teeth — the pitch — is chosen so that at least two or three teeth are always engaged in the work at once, keeping the cut smooth and the broach guided.
The pitch must suit the length of the cut: too coarse and only one tooth engages at a time, so the broach jerks and drifts; too fine and the tooth gullets cannot hold the chips. A common rule sets the pitch at about 1.75√L for a work length L, which for a 25 mm-long keyway gives a pitch near 8.75 mm and so about three teeth cutting together. Keeping two or three teeth engaged at all times means the load never falls onto a single tooth and the broach stays guided by the teeth already in the cut — the reason broached surfaces are so smooth and true. Each tooth’s gullet must also be deep enough to carry its chip clear through the whole stroke, since there is no chance to clear chips mid-pass.
Contents§4Cutting force
Because several teeth cut at once, each removing a full-width chip, the total force to drive a broach is large — the property that sizes the broaching machine.
The force is the number of teeth cutting at once, each times its chip cross-section and the material’s specific cutting force. For the keyway above — about 3 teeth engaged, 6 mm wide, rise per tooth 0.05 mm, in steel at roughly 2500 N/mm² — the force is 3 × 6 × 0.05 × 2500 = 2250 N. Wider forms, deeper cuts or more teeth in engagement raise it quickly, and internal broaches are loaded in tension as they are pulled, so the broach’s own cross-section must be strong enough not to snap under the pull. This is why broaching machines are rated by their pull or push force, and why the pitch is kept just fine enough for smoothness but no finer, to limit how many teeth load the tool at once.
§5Push and pull broaching
Broaches are driven two ways, and the choice follows from the fact that a bar is far stronger pulled than pushed.
A pull broach is drawn through the work in tension — long internal broaches for keyways, splines and holes are always pulled, because a long slender broach in tension cannot buckle, whereas in compression it would. A push broach is short and stout and driven in compression, used for shallow internal forms and for surface broaching of external shapes on a press; it must be short enough that it will not buckle under the push. So internal work of any depth is pull-broached, while short forms and external surfaces can be push-broached. In both, the broach travels once, linearly, and the shape is complete — the difference is only whether the tool is drawn or driven, set by its length and the buckling limit.
Contents§6Where broaching wins
Broaching is a production method: unbeatable for making an awkward internal or external form quickly and identically in quantity, uneconomic for one or two.
Its home is the high-volume production of shapes that are hard to make any other way — the internal keyway, the spline bore, the square or hexagon hole, the rifling in a barrel, external flats and fir-tree roots on turbine discs. Every part is identical because the shape lives in the tool, the cycle is a single fast stroke, and the finish and accuracy are excellent because the finishing teeth act like a broach-shaped reamer. Against that, a broach is expensive and made for exactly one form, so it pays only when the run is long enough — change the shape and the tool is scrap. Where those conditions hold, nothing matches broaching for fast, repeatable, accurate forms; where they do not, milling, slotting or wire EDM make the same shapes more cheaply in ones and twos.
Contents§7Quick reference
The working core of the page on one card rack.
Principle
stepped teeth, one stroke
each takes one layer
Rise per tooth
teeth = depth ÷ RPT
5 mm ÷ 0.05 → 100 teeth
Pitch
p ≈ 1.75√L
keep 2–3 teeth in cut
Force
F ≈ (teeth in cut)·w·RPT·k
Drive
pull (long, internal)
push (short, external)