Shaping, planing and broaching

Why it matters

Shapers, planers and slotters make flat surfaces, slots and keyways with cheap single-point tools — still useful in tool rooms, repair shops and for very long beds. Broaching is the opposite: a costly multi-tooth tool that finishes a keyway, spline or non-round hole in a single stroke in seconds, which makes it a mass-production favourite.

Key ideas

Shaper. The tool, on a reciprocating ram, cuts on the forward stroke; the work is clamped on the table, which is fed sideways between strokes. A crank-and-slotted-lever (Whitworth or slotted link) mechanism gives a quick return: the return stroke is faster than the cutting stroke because the crank turns through a larger angle during cutting. Hydraulic shapers give constant cutting speed and infinitely variable stroke rates. Shapers suit small to medium work (stroke up to roughly 900 mm).

Planer. The work, on a long table, reciprocates under a stationary tool; the tool is fed between strokes. Used for large, heavy, long work such as machine beds and slideways; several tool heads can cut at once.

Slotter (vertical shaper). Ram moves vertically; used for internal keyways, slots and internal profiles.

Cutting and return strokes. If the return-to-cutting time ratio is m (< 1), a fraction 1/(1 + m) of each cycle is spent cutting. The mean cutting speed is therefore higher than L·N would suggest. Material is only removed on the cutting stroke, so MRR is low compared with milling; this is why shaping and planing have largely given way to milling in production.

Broaching. A long tool with many teeth, each tooth standing slightly higher than the one before by the rise per tooth (the feed is built into the tool). Pulling (or pushing) the broach once through or over the work completes the cut: roughing teeth take most of the stock, semi-finishing teeth less, and finishing (sizing) teeth have no rise. Types: internal (holes, keyways, splines, square/hexagonal holes) and surface (external) broaching; pull and push broaches; continuous broaching for high volume.

• Advantages: very high productivity, good finish and accuracy (tolerance of a few tens of micrometres or better), relatively unskilled operation.
• Limitations: costly, job-specific tool (justified only for large batches); the surface must allow the broach to pass through (no blind holes for internal broaching); high forces need rigid fixturing; limited stock removal per tool.

Broach design ideas. Tooth pitch must leave enough gullet space for the chip curled up in it and keep at least two teeth engaged for steady cutting. A common empirical starting value is p ≈ 1.75√L (p and L in mm, L = length of work) — take actual values from a tool design handbook. Number of cutting teeth ≈ total depth ÷ rise per tooth.

Formulas

• V = L·N·(1 + m) / 1000 (mean cutting speed, m/min; L stroke length in mm; N strokes/min; m = return time / cutting time)
• Number of strokes = (W + allowance) / f (W width to be machined; f feed per stroke, mm)
• tm = number of strokes / N (min)
• MRR = f·d·Lw·N (mean MRR, mm³/min; d depth of cut, Lw length of work)
• Broaching: n_teeth = h / s (h total depth to remove, s rise per tooth, mm)
• p ≈ 1.75·√Lw (empirical pitch, mm); teeth engaged z = Lw / p (round up)
• F_max ≈ k·b·s·z (broaching force, N; k specific cutting pressure in N/mm² from data; b width of cut per tooth in mm)
• t = (L_broach + Lw) / V (broaching time for one stroke)

Worked examples

Example 1 (standard). A block 200 mm long and 150 mm wide is shaped with a stroke of 225 mm (200 mm plus 25 mm over-run), mean cutting speed 18 m/min, return-to-cutting time ratio 0.6, feed 0.5 mm/stroke, depth 3 mm. Allow 10 mm extra width for approach. Find the strokes per minute, machining time and mean MRR.

1. N = 1000·V / (L·(1 + m)) = 18 000/(225 × 1.6) = 50 strokes/min.
2. Number of strokes = (150 + 10)/0.5 = 320.
3. tm = 320/50 = 6.4 min.
4. MRR = f·d·Lw·N = 0.5 × 3 × 200 × 50 = 15 000 mm³/min.

Example 2 (GATE level). A keyway 10 mm wide and 3 mm deep is broached in a hub 40 mm long. Rise per tooth 0.05 mm, specific cutting pressure k = 3000 N/mm² (given), cutting speed 6 m/min. Estimate the number of roughing teeth, the pitch, the maximum broaching force and the cutting time.

1. n = h/s = 3/0.05 = 60 cutting teeth (plus a few zero-rise sizing teeth).
2. p ≈ 1.75√40 = 11.07 → take p = 11 mm.
3. Teeth engaged z = 40/11 = 3.6 → at most 4 teeth in contact.
4. Force per tooth = k·b·s = 3000 × 10 × 0.05 = 1500 N; F_max = 4 × 1500 = 6000 N.
5. Cutting length of broach ≈ 60 × 11 = 660 mm; stroke ≈ 660 + 40 = 700 mm = 0.7 m.
6. t = 0.7/6 = 0.117 min ≈ 7 s for the whole keyway.

Common mistakes

• Using V = L·N/1000 for a shaper, ignoring that only part of each cycle is cutting.
• Putting stroke length instead of work length in the MRR, or forgetting that MRR is a mean over both strokes.
• Treating the broach rise per tooth as a machine feed — it is ground into the tool.
• Counting zero-rise finishing teeth as cutting teeth when dividing the stock.
• Forgetting that maximum force depends on the number of teeth engaged at once, not the total number of teeth.
• Proposing broaching for a one-off part or a blind internal feature.

For GATE PI

• NAT on shaper/planer cutting speed with quick-return ratio, number of strokes and machining time.
• Broach design: number of teeth from rise per tooth, pitch, teeth in contact, force and power.
• MCQs comparing shaper, planer and slotter, and on the advantages and limitations of broaching.

Quick check

1. Stroke 300 mm, 50 strokes/min, return ratio 2/3 (return time ÷ cutting time). Mean cutting speed?
2. Width 120 mm, feed 0.4 mm/stroke. Number of strokes?
3. Total depth 2.4 mm, rise 0.06 mm/tooth. Roughing teeth?
4. Which machine moves the work, not the tool — shaper or planer?
5. Why must at least two broach teeth be engaged?

Answers: 1. 300 × 50 × (5/3)/1000 = 25 m/min. 2. 300. 3. 40. 4. Planer. 5. For steady cutting — a single tooth leaving one cut and entering the next causes force jumps and chatter.