Compute the pull force and cutting power of a multi-tooth broach in real time. Change the cut width, rise per tooth, specific cutting force, number of teeth engaged and broach velocity to size a broaching machine or design a new broach tool.
Parameters
Cut width b
mm
Width of the chip each tooth removes
Rise per tooth s_t
mm
Height step between consecutive teeth (feed per tooth)
How many teeth are cutting inside the workpiece at once
Broach velocity v_b
m/min
Typically 3-15 m/min; slower for finish teeth
Results
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Force per tooth F_tooth (N)
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Total pull force F_total (kN)
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Broach velocity v (m/s)
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Cutting power P (kW)
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Total chip area (mm²)
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Material removal rate (mm³/min)
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Broaching cross-section animation
The broach is pulled from left to right through the workpiece. Each tooth is s_t taller than the one in front; teeth currently inside the workpiece (highlighted) carry the cutting force F_tooth.
Per-tooth cutting force F_tooth, total pull force F_total and cutting power P. k_c is the specific cutting force [N/mm²], b is the cut width [mm], s_t is the rise per tooth [mm], n_e is the number of teeth engaged and v is the broach velocity [m/s].
Total chip area A_chip [mm²] and material removal rate MRR [mm³/min]. The simultaneous engagement of many teeth is what gives broaching its high removal rate without needing huge per-tooth chips.
Broaching Pull Force
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I have never heard of "broaching" before. How is it different from a lathe or a milling machine?
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Broaching is one of the most productive machining operations in mass-manufacturing. A "broach" is a long multi-toothed cutter — typically 0.5 to 2 metres long — that is pulled (or pushed) through the workpiece in a single stroke and finishes an internal keyway, a complex spline, a square hole or even an entire transmission gear-tooth profile in just a few seconds. Unlike turning or milling, where a single rotating tooth passes the same spot many times, in broaching every tooth on the bar passes the workpiece exactly once.
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Okay, but how does a long bar with teeth on it produce a complicated shape?
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The key is that each tooth is slightly larger than the one in front of it. The rise per tooth s_t is typically 0.02-0.10 mm — the default here is 0.05 mm. So the first tooth takes one chip, the second tooth takes another 0.05 mm chip, and so on for a hundred teeth or more. The last few teeth (the "finish teeth") have s_t = 0 and are literally the shape of the final form. When the last tooth has passed, the workpiece is left with exactly that shape, finished and to size in one stroke.
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So how big is the pull force? If a hundred teeth are cutting at once, that must be enormous.
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Good question. Only a handful of teeth are inside the workpiece at any given moment — that count is what you input as "teeth engaged n_e". The formula is simple: the force on one tooth is F_tooth = k_c · b · s_t and the total pull force is F_total = F_tooth · n_e. With the defaults (mild steel, b=25 mm, s_t=0.05 mm, k_c=2500, n_e=4), F_total = 2500 × 25 × 0.05 × 4 = 12,500 N — about 12.5 kN, well within a small horizontal broaching machine. For heavy internal broaches that cut large transmission gears, n_e can be 20+ and F_total can exceed 500 kN, which is why those broaches run on massive vertical machines with hydraulic rams buried in the floor.
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How is the cutting power decided? It seems like running faster should finish the job sooner, but the broach velocities are pretty slow.
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Right on the money. Power is just P = F · v — pull force times broach velocity. Broach speeds are slow compared to turning, typically 3-15 m/min, because each tooth still has to take its 0.05 mm chip without overheating. With the default v = 6 m/min (0.10 m/s) you get P = 12,500 × 0.10 = 1,250 W = 1.25 kW. Slide the v_b control on the "Cutting power vs broach velocity" chart and you will see power rises linearly with speed. On a real machine you divide by efficiency (0.7-0.85 for hydraulics) and add a 1.3-1.5 safety factor on the motor.
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If broaching is that efficient, why is not everything made this way?
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The catch is the cost of the broach itself. A 1.5 m internal transmission broach costs $20,000-$80,000 and has to be reground after a few thousand parts. So broaching only pays off when production volumes justify the tooling — typical break-even is 10,000-50,000 parts per year. For prototypes or small lots, milling or wire-EDM is much cheaper. On the upside, broaching routinely hits ISO IT7-IT8 dimensional accuracy and Ra 0.4-1.6 µm surface finish — usually good enough that no grinding is needed afterwards.
Frequently Asked Questions
It is the chip cross-section being cut at any instant multiplied by the specific cutting force k_c of the workpiece material. The force per tooth is F_tooth = k_c · b · s_t (b is the cut width and s_t is the rise per tooth), and with n_e teeth engaged simultaneously the total pull force is F_total = F_tooth · n_e. For example, broaching mild steel (k_c ≈ 2500 N/mm²) with b=25 mm, s_t=0.05 mm and n_e=4 gives F_total = 2500·25·0.05·4 = 12,500 N (12.5 kN), well within the range of a small horizontal broaching machine.
Cutting power is simply P = F · v, where F is the pull force in newtons and v is the broach velocity in m/s. Broach speeds are relatively low (3-15 m/min, i.e. 0.05-0.25 m/s) because the many teeth must each take a small chip to control temperature and wear. For F_total = 12,500 N and v = 6 m/min (0.10 m/s), P = 12,500·0.10 = 1,250 W = 1.25 kW. In practice you divide by the machine efficiency (0.7-0.85 for hydraulic broaching machines) and add a 1.3-1.5 safety margin when picking a motor.
The specific cutting force k_c depends on workpiece material and on the rise per tooth s_t. Typical values are: mild steel 2000-2500 N/mm², medium carbon steel (S45C / 1045) 2500-3000, alloy steel (SCM440 / 4140) 3000-3500, stainless (SUS304 / 304SS) 3500-4000, aluminium alloys 800-1500, cast iron 1500-2000. Because broaching uses very small s_t (0.02-0.05 mm), the apparent k_c is roughly 1.3-1.5 times larger than for plain turning (s = 0.2-0.5 mm) due to the size effect.
Broaches are expensive — an internal gear-form broach for an automotive transmission can be 1.5 m long, cost $20,000-$80,000 and must be reground every few thousand parts — so broaching only pays off in mass production. For complex internal forms such as transmission spline gears, broaching finishes one part in a few seconds, beating gear hobbing, EDM or shaping above roughly 10,000-50,000 parts per year. Below that range, wire-EDM or milling on a machining centre is usually cheaper.
Real-World Applications
Automotive transmission internal gears and splines: The internal gear teeth of manual transmissions and dual-clutch transmissions (DCTs) are cut by pulling a single 1.5 m gear-form broach through the part. The broach itself costs five figures, so this process is only used for high-volume parts (typically more than 100,000 per year). The IT7-class dimensional accuracy that the broach leaves on the gear directly determines how smoothly torque is transmitted.
Keyways in hubs, pulleys and gears: Cutting a keyway in the bore of a hub or pulley is the most common broaching application. Standard broaches (JIS B 1301 / DIN 6885) are available off the shelf for key widths of 6-25 mm and produce one keyway in 5-10 seconds on a small hydraulic press or horizontal broaching machine. Compared with end-milling a slot, the keyway sides are straighter and the edges are practically burr-free.
Rifle barrel rifling (rotary broaches): The helical grooves inside a rifle barrel can be cut with a rotary broach in a single pass. Modern barrels are increasingly made by cold hammer forging or by ECM, but high-precision target and hunting barrels are still broached, mostly with single-point or multi-tooth button-style rotary broaches.
Process planning and machine selection: Before ordering a new internal broach (a one-month lead time and a five-figure price tag), a quick calculation like this tool tells you whether the existing broaching machine has enough pull force and power. If the calculated F_total is already at the machine limit, the broach designer can revise the pitch (and hence n_e) or split the cut into multiple passes before any chips are made.
Common Misconceptions and Pitfalls
The biggest pitfall is ignoring the number of teeth engaged, n_e. As F_total = F_tooth · n_e shows, pull force scales directly with the number of teeth in contact. From the broach pitch p (tooth-to-tooth spacing) and the cut length L_cut, n_e ≈ L_cut / p + 1. For L_cut = 40 mm and p = 10 mm, n_e ≈ 5. Pitch is a balance: too tight raises n_e and pulls more force than the machine can handle; too coarse makes the broach far too long for the available stroke. Every new broach design should start with this n_e estimate.
Next, using a turning value of k_c for broaching. Broaches use a very small rise per tooth (0.02-0.05 mm) compared with turning (0.2-0.5 mm), and at small chip thicknesses the apparent specific cutting force is 1.3-1.5 times higher because of the so-called size effect. Using a turning-handbook value of k_c can under-predict the pull force by 30%, with the unpleasant result of the broach stalling halfway through the workpiece. The 2500 N/mm² default in this tool already represents mild steel at broaching-scale s_t.
Finally, the simple idea that "running the broach faster shortens the cycle". Cycle time is indeed inversely proportional to v_b, but broach life falls roughly with v_b to the 2nd or 3rd power. Once the finish teeth wear, the part dimensions and surface finish drop off a cliff, so cutting the time between regrinds from 5,000 parts to 1,000 parts makes broaching dramatically more expensive per part. Standard speeds are 6-10 m/min for mild steel, 3-5 m/min for stainless and 15-25 m/min for aluminium. Even if this tool says you have power to spare, do not just push v_b higher.
How to Use
Enter the cut width (mm) in the broach range field—typical values span 10–80 mm for automotive gear broaches
Set rise per tooth (mm/tooth) between 0.05–0.3 mm; finer feeds reduce tool chatter on cast iron
Input specific cutting force k_c (N/mm²) based on material: 1800 N/mm² for ductile iron, 2200 N/mm² for steel alloys
Specify number of effective teeth and broach velocity (m/min); industrial broaches typically operate 8–15 m/min
Read total pull force in kN, force per tooth in N, cutting power in kW, and material removal rate in mm³/min
Worked Example
Broaching a keyway in SAE 1045 steel with k_c = 2100 N/mm², cut width b = 25 mm, rise per tooth f = 0.12 mm/tooth, 12 effective teeth, velocity 10 m/min. Total chip area = 25 × 0.12 × 12 = 36 mm². Force per tooth = 36 × 2100 = 75,600 N. Total pull force = 75.6 kN. Cutting power = (75.6 × 10) / 60 = 12.6 kW. Material removal rate ≈ 43,200 mm³/min.
Practical Notes
On gray cast iron (k_c ≈ 1200 N/mm²), reduce velocity to 6–8 m/min to prevent broach edge wear and chatter in deep slots
Oversized pull forces (>100 kN) indicate inadequate coolant flow or excessive rise per tooth; dial back feed by 20% and resurface the broach
Monitor power consumption; aluminum alloys demand 40–50% less power than steel at identical speeds, enabling faster feeds
Tooth contact length and workpiece hardness variation directly scale cutting force; soften material at 650–700°C prior to broaching hard zones