Tool life at any cutting speed from the Taylor equation, the parts you get per cutting edge, cost and time per part, and the cutting speeds for the lowest cost and for the highest output. Start from the speed your insert catalogue gives for 15 minutes of tool life.
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| Cutting speed | Tool life | Parts per edge | Time per part | Cost per part |
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Taylor's tool-life equation says that raising the cutting speed shortens the life of the edge much faster than it shortens the cut. Faster cutting saves machine time, but needs more edges and more edge changes. The cost per part therefore has a minimum, and the speed for the highest output lies above it.
The economics follow Gilbert's classic analysis as given in Groover, Fundamentals of Modern Manufacturing (chapter 23), Kalpakjian and the Machinery's Handbook section on machining econometrics; tool-life testing itself is defined in ISO 3685. Typical exponents: HSS n ≈ 0.125, uncoated carbide n ≈ 0.25, coated carbide n ≈ 0.3, ceramics n ≈ 0.6. Insert catalogues (for example Sandvik Coromant) give cutting speeds for 15 minutes of tool life. The Taylor equation is only reliable near the speeds where it was measured, so treat results far from the catalogue speed as a trend and confirm them on the machine.
This calculator applies Taylor's tool-life equation to a real job. From the cutting speed your insert catalogue gives for a known tool life (usually 15 minutes), it predicts the tool life at any other speed, the parts per cutting edge, and the cost and time per part including edge changes. It also finds the cutting speed for the lowest cost per part and the speed for the highest output. Production engineers, CNC programmers and students use it to choose a cutting speed on economic grounds instead of habit.
The catalogue speed is already within 1 % of the lowest cost. Running at 374 m/min would raise output by about 4 % but needs an edge change every 8 parts instead of every 29.
Taylor found that cutting speed V and tool life T follow V × T^n = C, where n depends mainly on the tool material and C on the tool and workpiece pair. It means tool life falls steeply with speed: with carbide (n ≈ 0.25), 20 % more speed cuts the tool life roughly in half. The equation holds within the range of speeds where it was measured.
Typical values are about 0.125 for high-speed steel, 0.25 for uncoated carbide, 0.3 for coated carbide and 0.6 for ceramics, with wide ranges depending on the material cut. You can measure n yourself: note the tool life T1 and T2 at two speeds V1 and V2, then n = ln(V1/V2) / ln(T2/T1).
Minimise the cost per part, which adds machine time, tool cost and edge-change time. The minimum is at tool life T = (1/n − 1) × (tool change time + edge cost / machine rate per minute), and the speed follows from Taylor: V = C / T^n. Expensive edges or cheap machine time push the speed down; expensive machines push it up.
If only output counts, the best tool life is T = (1/n − 1) × tool change time, which is always shorter than the lowest-cost tool life. For carbide with a 1 minute edge change that is 3 minutes. The speed is higher than the economical one, so each part costs a little more but more parts leave the machine per hour.
Most insert catalogues, for example Sandvik Coromant's, give recommended cutting speeds for 15 minutes of tool life in the cut. This calculator uses that point to fix the Taylor constant, so you can enter the catalogue speed and 15 min directly and see what other speeds would give.
Around the economical speed the time saved by cutting faster is almost exactly balanced by the extra edges and edge changes, so the cost per part changes little over a range of perhaps ±10–15 %. That is why it is safe to choose a round speed near the optimum, and why process stability often matters more than the exact speed.
What you need to build, measure or check the result.
Inspection loupe 10xJudge flank wear on the edgeView on Amazon →
Carbide turning inserts CNMGEdges the cost per part is built onView on Amazon →
Digital caliperWatch size drift as the edge wearsView on Amazon →As an Amazon Associate I earn from qualifying purchases. Prices and availability are shown on Amazon.