Every broaching job comes down to one question before anything else: does the machine have the force to pull the broach through the part in one stroke? Order too little tonnage and the slide stalls mid-cut, the broach chips or snaps, and the workpiece is scrapped inside the machine. Order too much and you pay for frame, hydraulics and floor space you will never use. Tonnage is also the single biggest price driver on a broaching machine, so a disciplined estimate pays for itself twice — once in the purchase decision and once in avoided downtime.
This guide shows the full calculation: the broaching force formula, the unit cutting resistance of the common workpiece materials, a six-step working method, three fully worked examples (a keyway in carbon steel, a spline in alloy steel, and a round hole in cast iron), the safety margin that separates a textbook answer from a shop-floor answer, and the mistakes that most often wreck the estimate.
The Broaching Force Formula
The starting point is the force the cut itself generates. Broaching is unique among cutting processes because the feed is built into the tool: each successive tooth rises by the tooth lift, so the machine has no feed dial to turn down if the cut proves too heavy. The force must be known before the stroke starts. The expected broaching force is:
Expected Broaching Force (kgf) = Cutting Width (mm) × Cutting Depth per Tooth (mm) × Cutting Resistance per Unit Area (kgf/mm²) × Number of Simultaneous Cutting Teeth
Each variable is measurable from the drawing and the broach:
- Cutting width is the total length of edge engaged in the cut. For a keyway it is the keyway width; for a spline it is the sum of all tooth flank widths cutting at once; for a round hole it is the circumference of the bore, π × diameter.
- Cutting depth per tooth is the tooth lift — the amount each tooth rises above the one before it. It is set by the broach designer, typically between 0.01 and 0.10 mm depending on the broach type and material.
- Cutting resistance per unit area is a material property: how much force the material pushes back per square millimetre of chip cross-section. It ranges from roughly 100 kgf/mm² for light alloys to 400 kgf/mm² for alloy steel, as tabulated below.
- Number of simultaneous cutting teeth is how many broach teeth are inside the workpiece at the same moment — workpiece length divided by tooth pitch, rounded down. A longer part or a finer pitch puts more edges in the cut and multiplies the force accordingly.
The formula gives the expected force under normal conditions. It is not the number you size the machine to, because it assumes a sharp broach, uniform material and steady lubrication. The sizing number applies a safety factor:
Max Allowable Broaching Force (kgf) = 1.8 × Expected Broaching Force (kgf)
The 1.8 multiplier absorbs the real-world conditions the formula cannot see: edge wear over the broach’s service life, hardness scatter within a material batch, and the break-in torque of a cold machine. The machine’s rated tonnage must meet or exceed this maximum force, not the expected one.
Tooth Lift Ranges and Unit Cutting Resistance by Material
The table below collects the standard tooth lift ranges (cutting depth per tooth) and the unit cutting resistance for the five material families most often broached. Use the tooth lift range that matches your broach type — round, spline or surface — and take the cutting resistance for your material. When a material sits between two rows, or the batch hardness runs high, use the higher resistance value.
| Material | Round Broach — Tooth Lift (µm) | Spline Broach — Tooth Lift (µm) | Surface Broach — Tooth Lift (µm) | Cutting Resistance per Unit Area (kgf/mm²) |
|---|---|---|---|---|
| Alloy Steel | 10~20 | 25~30 | 30~70 | 300~400 |
| Steel | 10~20 | 25~35 | 30~70 | 300 |
| Cast Iron | 25~40 | 25~40 | 50~75 | 200 |
| Malleable Cast Iron | 25~35 | 25~35 | 50~75 | 150~200 |
| Light Alloy Metal | 25~35 | 30~40 | 60~100 | 100~200 |
Two patterns in the table are worth internalizing. First, tougher materials not only resist the cut more per square millimetre but are also broached with a finer tooth lift — alloy steel takes roughly a third of the lift that cast iron does on a round broach — so force grows through resistance while the designer compensates through lift. Second, cast irons cut freely (200 kgf/mm² and below) but tolerate a much coarser lift, which is why a cast-iron round hole and a steel spline of the same width can end up needing surprisingly similar tonnage.
Six Steps to Calculate Broaching Machine Tonnage
Step 1: Determine the broaching process parameters
Collect the dimensions that define the cut: the pre-machined hole diameter or the surface to be broached, the workpiece length in the cutting direction, the keyway width or spline tooth counts and flank widths. These come straight off the part drawing. Then obtain the broach specification sheet and note the tooth lift and the tooth pitch — the spacing between successive cutting teeth.
Step 2: Calculate the cutting area
Establish the material cross-section each tooth removes and the total engagement width. For a round hole, the per-tooth chip area is the tooth lift multiplied by the bore circumference, and the gross cutting area for the pass is π × (hole diameter + tooth lift) × broaching length. For keyways and splines the widths read directly from the drawing. The engagement width times the tooth lift gives the chip area per tooth — the quantity the material resistance acts on.
Step 3: Determine material properties
Find the tensile or yield strength of the workpiece material, either from the mill certificate or from a test coupon, and locate the material in the table above to read its cutting resistance per unit area. Where the certificate shows hardness near the top of the normal band, take the upper resistance figure — a 30-point Brinell difference between batches is enough to move steel from 300 toward 400 kgf/mm² in practice.
Step 4: Estimate the broaching force
Apply the formula: broaching force = cutting coefficient (the unit cutting resistance) × cutting area, extended across every tooth engaged at once. Multiply the engagement width by the tooth lift and the cutting resistance to get the force per tooth, then multiply by the number of simultaneous cutting teeth — workpiece length ÷ tooth pitch, rounded down to the whole tooth.
Step 5: Apply the safety factor and machine transmission efficiency
Two adjustments convert cutting force into machine demand. First, multiply by 1.8 for the maximum allowable broaching force, covering tool wear and material variation. Second, divide by the machine’s transmission efficiency: hydraulic broaching machines typically run 0.7–0.9 depending on the age and condition of the seals, pumps and guide ways. The force at the workpiece is always less than the force the machine must generate internally.
Step 6: Calculate the tonnage and select the machine class
Machine tonnage = maximum allowable broaching force ÷ transmission efficiency, converted to tonnes (1 tonne = 1,000 kgf). Round up to the next standard machine rating — manufacturers build in discrete steps, and the rounding you do here is the cheapest capacity margin you will ever buy. The three worked examples below run the full chain from drawing to machine class.
The result of the six steps is an estimate, not a guarantee. Broaching speed, progressive tool wear over the sharpening cycle, and the quality of coolant delivery all shift the real force around the calculated value. How speed and chip load interact is covered in broaching speed vs. feed, and the force consequences of running a broach to the end of its tool life are covered in broach tool life.
Worked Example 1: Keyway in Medium-Carbon Steel (Arbor Press)
A hub in 1045-class medium-carbon steel needs a single 10 mm keyway. The bore length is 70 mm, the broach has a 14 mm tooth pitch, and the designer set a 0.03 mm (30 µm) tooth lift — inside the 25~35 µm spline-type band for steel. The cutting resistance for steel is 300 kgf/mm².
- Cutting width = keyway width = 10 mm
- Teeth in cut = bore length ÷ pitch = 70 ÷ 14 = 5 teeth
- Expected force = 10 × 0.03 × 300 × 5 = 450 kgf
- Maximum allowable force = 1.8 × 450 = 810 kgf ≈ 0.81 tonne
A 1–2 tonne arbor or hydraulic press covers this job with margin, which is exactly why small keyway work is so often done on a press instead of a full broaching machine. Tooling and process details for this class of job are covered in the keyway broaching complete guide, and suitable machines are listed on the keyway broaching machine page.
Worked Example 2: Spline in Alloy Steel (Vertical Broaching Machine)
A gear hub in 4140-class alloy steel needs an 8-tooth internal spline. Each tooth flank is 6 mm wide, so the total cutting width is 8 × 6 = 48 mm. The bore is 90 mm long, the broach pitch is 15 mm, and the tooth lift is 0.028 mm (28 µm), matching the 25~30 µm alloy-steel spline band. Because this is a high-strength material, the calculation takes the upper cutting resistance of 400 kgf/mm².
- Cutting width = 8 teeth × 6 mm = 48 mm
- Teeth in cut = 90 ÷ 15 = 6 teeth
- Expected force = 48 × 0.028 × 400 × 6 = 3,225.6 kgf ≈ 3.23 tonnes
- Maximum allowable force = 1.8 × 3,225.6 = 5,806 kgf ≈ 5.81 tonnes
- Machine demand at 0.8 transmission efficiency = 5,806 ÷ 0.8 = 7,257 kgf ≈ 7.26 tonnes
The calculation lands between ratings, so the purchase decision rounds up to a 10-tonne class machine — the standard step that leaves room for a harder batch or a re-sharpened, slightly rougher broach. Internal splines of this size are classic vertical broaching machine work; the machine architecture is explained in what is a vertical broaching machine.
Worked Example 3: Round Hole in Gray Cast Iron
A cast-iron housing needs a finished 40 mm round bore, 50 mm deep. For a round broach the cutting width is the bore circumference: π × 40 = 125.7 mm. The tooth lift is 0.03 mm (30 µm) from the 25~40 µm cast-iron round-broach band, the pitch is 12.5 mm, and the cutting resistance is 200 kgf/mm².
- Cutting width = π × 40 = 125.7 mm
- Teeth in cut = 50 ÷ 12.5 = 4 teeth
- Expected force = 125.7 × 0.03 × 200 × 4 = 3,016.8 kgf ≈ 3.02 tonnes
- Maximum allowable force = 1.8 × 3,016.8 = 5,430 kgf ≈ 5.43 tonnes
- Machine demand at 0.85 efficiency = 5,430 ÷ 0.85 ≈ 6,388 kgf ≈ 6.39 tonnes
Even though cast iron cuts at only 200 kgf/mm² — half the resistance of the alloy steel in Example 2 — the wide circumference of the round cut brings the tonnage demand to nearly the same neighborhood. This is the most common surprise in tonnage estimating: material resistance and engagement width trade off against each other, and neither can be judged alone.
What Changes the Force in Practice
The formula’s variables are fixed by the drawing and the tool, but four shop-floor factors move the real force around the calculated value, and every one of them pushes upward:
Material condition
Work-hardening alloys and batches at the top of the hardness band cut heavier than the nominal resistance value. The spread inside the alloy-steel row itself — 300 to 400 kgf/mm² — is a 33% force difference before any other factor is considered. If your certificates show high hardness, calculate with the top of the band.
Broach sharpness
A dull edge does not slice — it ploughs. Cutting force rises steadily as the edge wears, which is precisely why the sizing rule multiplies expected force by 1.8 rather than leaving headroom of 10 or 15%. A broach at the end of its sharpening interval can demand a substantially larger force than the same broach fresh off the grind. The wear progression is documented in broach tool life, and the point at which a regrind becomes due is covered in when to re-sharpen a broach tool.
Cooling and lubrication
Cutting fluid does three jobs at once in broaching: it evacuates chips from the deep, enclosed cutting zone, it reduces friction along the tooth flanks, and it carries heat out of the edge. Starve the cut of coolant and friction force stacks on top of cutting force — a common cause of machines that pulled the job comfortably for years and then begin stalling after a coolant nozzle is relocated or a filter clogs.
Tooth lift selection
Tooth lift is the one variable the broach designer can trade. A coarser lift removes the allowance with fewer teeth, making a shorter, cheaper broach — but force rises in direct proportion. A finer lift cuts force but lengthens the broach, which lengthens the stroke and can exceed the machine’s pull length. The interaction between lift, speed and surface finish is treated in broaching speed vs. feed; on the machine side, tooth pitch is what sets how many teeth share the load at any instant.
From Tonnage to Machine Selection
A tonnage number on its own does not buy a machine. Five further checks turn the calculation into a specification:
- Part size and stroke length. The machine’s stroke must cover the broach length plus the part, not merely reach the tonnage figure. Large or complex parts can demand a bigger frame than the force calculation alone suggests.
- Accuracy requirement. Fine-pitch splines and tight concentricity calls run better on a stiffer, higher-tonnage frame, where the cut is a smaller fraction of the machine’s capacity and deflection stays low.
- Production volume. High-volume lines justify tonnage and rigidity margin to hold capability over three shifts; small batches can size closer to the calculation to control cost.
- Existing capacity. Before adding a machine, check whether a current machine’s rating already covers the new job’s maximum allowable force — the cheapest tonnage is the tonnage you already own.
- Budget. Tonnage is the primary cost driver of a broaching machine. Sizing honestly — sharp pencil on the formula, then the standard rounding step — keeps the budget matched to the work. Budget planning is covered in the broaching machine price guide.
The full selection method — machine types, configuration trade-offs and the questions to ask a supplier — is laid out in how to choose the right broaching machine. For internal work of the kind in the examples above, the vertical broaching machine is the most common configuration; horizontal machines earn their place on long strokes and automotive-scale lines.
Common Calculation Mistakes
Four errors account for most under-sized broaching machines and most snapped broaches:
- Using the bottom of the material’s resistance band. Calculating alloy steel at 300 kgf/mm² when the incoming batch warrants 400 kgf/mm² understates the force by a third before the safety factor is even applied. When in doubt, size with the top of the band.
- Ignoring tool wear. Sizing to the expected force of a sharp broach — skipping the 1.8 factor — builds a machine that is adequate on day one and marginal two resharpenings later. The factor exists precisely because a worn broach cuts with more force; see when to re-sharpen a broach tool.
- Forgetting transmission efficiency. The rated tonnage is delivered at the cutting edge only after losses through hydraulics and guide ways. Dividing by 0.7–0.9 is not pessimism; it is arithmetic.
- Miscounting simultaneous teeth. Using the total tooth count instead of teeth-in-cut, or rounding the pitch division up instead of down, inflates the force estimate and pushes buyers into an oversized, over-budget machine. Count only the teeth inside the part at one moment: length ÷ pitch, rounded down.
FAQ
How much tonnage do I need for broaching?
It depends entirely on the cut, and the examples above show the spread: a 10 mm keyway in carbon steel needs under a tonne at the tool, a mid-size spline in alloy steel pushes a 10-tonne class machine, and a 40 mm cast-iron bore lands in between. Run the six-step calculation for your specific part — width, tooth lift, material resistance and teeth in cut — rather than sizing from a rule of thumb.
How is broaching force calculated?
Expected broaching force = cutting width × cutting depth per tooth × cutting resistance per unit area × number of simultaneous cutting teeth, all in mm and kgf/mm². Multiply by 1.8 for the maximum allowable force, then divide by the machine’s transmission efficiency (0.7–0.9) and convert to tonnes (1,000 kgf = 1 tonne).
What happens if the tonnage is too low?
The slide loses velocity through the cut or stalls partway, chips stop clearing, and force concentrates on whichever teeth are still engaged — which chips edges, snaps the broach and can scrap the workpiece with the tool stuck inside it. Low tonnage also shows up as torn surface finish and undersized, bell-mouthed holes before any catastrophic failure. A machine that stalls on the first part of a batch should be treated as an estimate error, not a machine defect.
How does a dull broach affect required tonnage?
A dull broach ploughs instead of shearing, so the same chip cross-section demands more force — the reason the sizing rule carries a 1.8 safety factor on top of the sharp-tool calculation. In service this means a job that ran comfortably can approach the machine’s limit as the broach wears toward its regrind point. Tracking force (or motor current) per stroke is a practical way to schedule broach re-sharpening before the machine becomes the limiting component.
Put the Number to Work
Calculate the maximum allowable force for your heaviest part, add the transmission efficiency, and round up to the next standard rating — that single number steers the whole purchase. Browse the machine range by tonnage class on the broaching machines catalogue page, work through the selection framework in how to choose the right broaching machine, and cost the decision with the broaching machine price guide.
