# Speeds and feeds **Speeds and feeds** are the two velocities that define a machining operation: the *cutting speed*, the rate at which the cutting edge moves past the surface of the work, and the *feed rate*, the rate at which the tool and the work advance into each other. Together with the depth of cut they fix how much metal comes off per minute, how hot the edge runs, how long the tool lasts and what finish the surface carries. The cutting speed is a property of the pairing between the work material and the tool material, chosen from tables built up over a century of shop experience; the spindle speed that delivers it depends on the diameter of the tool or the work, and the feed follows from the number of cutting edges and the chip each is allowed to take. [[Milling_(machining)|Milling]], turning and drilling all run on the same three numbers, and a [[Computer_numerical_control|CNC]] program is, at bottom, a list of positions with a speed and a feed attached to each.[^virasak-cnc] In the microsim below the reader changes the diameter *D* of an end mill between 1/16 and 1 inch on a logarithmic slider, and picks a work material whose cutting-speed band comes from the 29-row table in *Manufacturing Processes 4-5*. The shop rule `RPM = CS·4/D` draws the spindle speed as a hyperbola inside the material's band, the exact form `12·CS/(π·D)` runs dashed beside it, and the feed `IPM = F·N·RPM` is read out for a two-flute cutter; the book's own example, 90 surface feet per minute on a 3/8-inch cutter giving 960 RPM and 3.84 inches per minute, is the default. On the [[Materials_science|Materials science]] flagship this article is the *Machining: speeds and feeds* section of Part IV, Fundamentals › Processing, the processing counterpart of the [[Work_hardening|work hardening]] page that explains why some rows of the table are so slow. ## Cutting speed The cutting speed is "the speed at the outside edge of the tool," also called the surface speed, and the American shop quotes it in [[Surface_feet_per_minute|surface feet per minute]] (SFM); at the same spindle speed a larger cutter has the higher surface speed, because its rim travels farther per turn.[^virasak-p29] It is the speed the cutting edge sees, and the edge does not care whether the tool spins past a stationary block, as in milling and drilling, or the work spins past a stationary tool, as in turning. What the edge does care about is the material it is shearing and its own resistance to [[Heat|heat]] and [[Wear|wear]]. A harder work material calls for a slower cutting speed, and the book orders [[Steel|steel]], [[Iron|iron]], [[Aluminium|aluminium]] and lead by increasing permissible speed; a harder tool material allows a faster one, from [[Carbon_steel|carbon steel]] through high-speed steel to carbide.[^virasak-p29] The manual's Table 1 collects the bands, and a selection of its 29 rows shows how wide the spread is:[^virasak-table1] | work material | cutting speed (SFM) | |---|---| | low-carbon steel | 40–140 | | free-machining steel | 100–150 | | tool steel | 40–70 | | stainless steel 302/304 | 60 | | cast iron, regular | 80–120 | | aluminium alloys | 300–400 | | copper | 100–500 | | bronze, hard | 30–70 | | titanium alloy | 20–60 | | Inconel; cobalt-base alloys | 5–10 | From Inconel's 5 to copper's 500 is a factor of a hundred. The slow rows are the materials that [[Work_hardening|work-harden]] rapidly, hold their strength at the temperature of the cut, or both: the [[Superalloy|nickel superalloys]], the austenitic [[Stainless_steel|stainless steels]] and [[Titanium|titanium]]. The fast rows, [[Copper|copper]], [[Brass|brass]] and aluminium, are soft and conduct heat away from the edge; [[Cast_iron|cast iron]] sits in the middle. The bands are guidance for a rigid setup and a sharp tool, and the table does not say which tool material it assumes beyond the worked example's high-speed steel; single values such as the stainless steels' 60 are points, not ranges.[^virasak-table1][^manual12] ### Machinability rating The table's ordering is a rough [[Machinability|machinability]] ranking, and machinability ratings formalize it: a reference free-machining steel is assigned a rating of 100 %, and other materials are rated by the cutting speed at which they give the same tool life under the same conditions, so that a 70 % material is machined at roughly 70 % of the reference speed.[^machinery] The rating bundles together properties that do not always move together, the work material's [[Hardness|hardness]] and strength, its rate of work hardening, its [[Thermal_conductivity_and_resistivity|thermal conductivity]], which decides how much of the cutting heat stays in the chip and how much reaches the edge, and its abrasiveness, so a rating is a summary for a family of operations rather than a physical property. Free-machining steels earn their rating from sulfur or lead additions that break the chip and lubricate the cut, which is why the table places them above plain low-carbon steel.[^virasak-table1] ## Spindle speed The spindle speed is the rotation rate, in revolutions per minute, of the spindle that carries the cutter (on a mill or drill press) or the work (on a lathe). It is the number the machinist actually sets, on a belt-and-pulley machine by moving the belt between steps, on a geared or variable-speed head by a dial, and on a CNC machine by an S word in the program. The cutting speed is what the material wants; the spindle speed is how the machine delivers it, and the conversion between them is a matter of geometry. A point on the rim of a cutter of diameter *D* travels `π·D` per revolution, so the surface speed is `π·D·RPM`, and holding the surface speed constant while the diameter changes means turning a small tool fast and a large one slowly. The same relation is the reason a lathe facing a large disc must speed up as the tool approaches the centre if it is to keep a constant cutting speed, which modern CNC lathes do automatically. ### Spindle speed calculations The shop form of the conversion, in the units the table uses, is the microsim's headline equation:[^virasak-rpm] `RPM = (CS × 4) / D` with CS the cutting speed in surface feet per minute and *D* the tool diameter in inches. The book's example takes a cutting speed of 90 for mild steel and a 3/8-inch high-speed-steel two-flute end mill: `RPM = 90 × 4 / 0.375 = 960`.[^virasak-rpm] The exact form of the same conversion is `RPM = 12·CS/(π·D) = 3.82·CS/D`, since a foot is 12 inches and the rim travels `π·D` inches per turn; the constant 4 is a shop rounding that reads about 4.7 % high, and the exact answer to the example is 917 RPM (derived). The sim draws both: the rule as a solid hyperbola, the exact form dashed beside it, close enough that the difference never matters on a machine whose speed steps are coarser than that. What matters is the hyperbola itself. Halving the tool diameter doubles the spindle speed needed, and the sim's logarithmic slider makes a 1/16-inch cutter in the same mild steel call for 5,760 RPM while a 1-inch cutter needs 360 (derived). Changing the material preset shifts the whole band. At the same 3/8-inch diameter the book's table gives Inconel 53–107 RPM, titanium alloy 213–640, low-carbon steel 427–1,493, regular cast iron 853–1,280, aluminium alloys 3,200–4,267 and copper 1,067–5,333 RPM (derived from the Table 1 bands). Two of the manual's unit-test questions work the same way: a 1/2-inch end mill in aluminium alloys wants 2,400–3,200 RPM, and a 3/4-inch end mill in [[Bronze|bronze]] 480–800 RPM for the regular grade or 160–373 for the hard one (derived).[^virasak-q] "Mild steel" is not itself a row of the table, and its 90 SFM falls inside both the low-carbon and medium-carbon bands, so the sim keeps the example as an example rather than mapping it to a row.[^manual12] The formula is the same for a drill, with *D* the drill diameter, and for turning, with *D* the diameter of the work at the cut. ## Feed rate The feed is "the distance in inches per minute that the work moves into the cutter," and on the milling machines the manual describes it is set independently of the spindle speed, which "permits faster feeds for larger, slowly rotating cutters."[^virasak-feed] Eight considerations set it: the depth and width of cut, the type and sharpness of the cutter, the work material, its strength and uniformity, the finish and accuracy required, and the rigidity of the machine, the workholding and the tooling.[^virasak-feed] A feed too light rubs instead of cutting, dulls the edge and work-hardens the surface for the next pass; a feed too heavy overloads the edge, deflects the tool and sets it chattering in [[Vibration|vibration]]. The right feed is therefore not a single number but a chip thickness, the *feed per tooth*, "the amount of material that should be removed by each tooth," chosen so that each tooth advances equally and produces "chips of equal thickness."[^virasak-feed] For end mills the book puts it between 0.001–0.002 inch per tooth for very small cutters in steel and 0.010 inch per tooth for large cutters in aluminium.[^virasak-feed] ### Formula to determine feed rate The feed rate follows from the chip load, the number of teeth and the spindle speed:[^virasak-feed] `IPM = F × N × RPM` with IPM the table feed in inches per minute, *F* the feed per tooth in inches and *N* the number of teeth. Continuing the example, a 0.002-inch chip load on a two-flute cutter at 960 RPM gives `IPM = 0.002 × 2 × 960 = 3.84` inches per minute, the sim's readout.[^virasak-feed] The multiplication is the whole lesson: *F* is the chip each tooth takes, and the feed rate simply multiplies it by the number of teeth passing per minute, so a four-flute cutter at the same chip load and speed feeds 7.68 inches per minute without taking a thicker chip, and the same two-flute cutter at the aluminium end of the chip-load range, 0.010 inch per tooth, feeds 19.2 inches per minute (derived). Drilling machines with power feed specify the feed per revolution instead: set to 0.006 inch, "the machine will feed .006" for every revolution," so at 960 RPM the drill advances 5.76 inches per minute (derived).[^virasak-ipr] The two rates must not be confused, because a feed per revolution is multiplied by the spindle speed and a feed per minute is not.[^manual12] ## Depth of cut The depth of cut is the third dimension of the operation, the thickness of the layer removed in one pass, and with the width of cut it is the first item on the manual's list of factors that set the feed.[^virasak-feed] Depth, width and feed rate multiply to the volume removed per minute, the material removal rate: a 3/8-inch slot cut 0.100 inch deep at the example's 3.84 inches per minute removes 0.144 cubic inches per minute (derived, with an illustrative depth). Roughing takes the deepest cut the machine, the tool and the workholding will stand, because removing metal in few passes is cheaper than in many; finishing takes a light cut at a fine feed, because the finish, not the removal rate, is the object. A deep cut also spreads the heat and the wear along more of the cutting edge, which is why a light finishing cut that uses only the tip can wear a tool faster per unit volume than a heavy one. In turning, each pass reduces the work's diameter by twice the depth of cut, and every pass lowers the diameter at which the next cutting speed must be computed. ## Interrelationship of theory and practice The speed table is empirical, and the reason it works is that it hides a physical law. In 1907 [[Frederick_Winslow_Taylor|Frederick Winslow Taylor]] published the results of a quarter-century of cutting experiments, including the relation between cutting speed and tool life that bears his name, `V·Tⁿ = C`, in which a small increase in speed *V* costs a large decrease in the minutes *T* a tool lasts, with an exponent *n* that depends on the tool material.[^taylor1907] A cutting-speed table is a cross-section of that law at an economic tool life, and the width of each band in Table 1 is the room the machinist has to trade tool life for production. Mid-century research explained the mechanics behind the numbers: Merchant's shear-plane model treats the chip as formed by shear along a single plane ahead of the edge, and relates the cutting force to the shear strength of the work, the rake angle and the [[Friction|friction]] on the tool face.[^merchant1945] The feed enters the finish through geometry, since a single-point tool of nose radius *r* leaves a scalloped surface whose theoretical peak-to-valley height is `f²/(8·r)` for a feed *f* per revolution, a standard relation that is not in the manual but is why a finishing pass runs at a fine feed.[^kalpakjian] In practice the calculated numbers are the beginning of a conversation with the machine. The manual's own pitfalls apply: the constant 4 is a rounding, the table's bands are wide, the tool material is only implied, and the rigidity of the setup, which the formulas never see, decides whether the top of a band is usable at all.[^manual12] Coolant and [[Lubrication|lubrication]] move the whole picture, since a flood coolant carries heat away from the edge and lets it run faster, and the same manual's tapping unit prescribes a low 60 RPM in low gear for power tapping precisely because a tap cannot shed its heat or its chips.[^virasak-tap] The lathe chapter repeats the calculation for turning, where the relevant diameter is the work's rather than the tool's.[^virasak-lathe] ## Academic research examples Taylor's tool-life law is the founding example of machining research, and its exponent is still measured for every new tool material, from high-speed steel through coated carbides to [[Ceramic|ceramics]] and polycrystalline [[Diamond|diamond]].[^taylor1907] Merchant's 1945 papers turned the cut into a problem in mechanics that could be solved on paper, and their orthogonal-cutting geometry remains the standard first model of chip formation.[^merchant1945] Later work has followed the same pattern of one controlled variable at a time, measuring tool wear, cutting force, [[Temperature|temperature]] and surface roughness against speed, feed and depth of cut, and the microsim's discipline of one control and one readout is the same experiment reduced to arithmetic. The manual's own contribution to the research tradition is humbler and older: a table of numbers that a hundred years of tool makers and machinists have agreed will not break the tool.[^virasak-table1] *See also:* [[Machinability]] · [[Milling_(machining)]] · [[Surface_feet_per_minute]] · [[Computer_numerical_control]] · [[Work_hardening]] · [[Wear]] · [[Manufacturing]] ## References [^virasak-p29]: Virasak, LamNgeun (2019). *Manufacturing Processes 4-5*. Open Oregon Educational Resources (Portal Book 094). Chapter 1, Unit 2: Speeds, Feeds, and Tapping, cutting speed defined and the material and tool orderings, p. 29. https://open.umn.edu/opentextbooks/textbooks/manufacturing-processes-4-5 [^virasak-table1]: Virasak, LamNgeun (2019). *Manufacturing Processes 4-5* (Portal Book 094). Chapter 1, Unit 2, Table 1, cutting speeds in surface feet per minute (29 rows), p. 30. https://open.umn.edu/opentextbooks/textbooks/manufacturing-processes-4-5 [^virasak-rpm]: Virasak, LamNgeun (2019). *Manufacturing Processes 4-5* (Portal Book 094). Chapter 1, Unit 2, the spindle-speed formula RPM = CS × 4 / D and the 3/8-inch, 90 SFM, 960 RPM example, pp. 30–31. https://open.umn.edu/opentextbooks/textbooks/manufacturing-processes-4-5 [^virasak-feed]: Virasak, LamNgeun (2019). *Manufacturing Processes 4-5* (Portal Book 094). Chapter 1, Unit 2, feed defined, the eight factors, feed per tooth, IPM = F × N × RPM, the 3.84 IPM example and the 0.001–0.010 inch per tooth range, p. 31. https://open.umn.edu/opentextbooks/textbooks/manufacturing-processes-4-5 [^virasak-ipr]: Virasak, LamNgeun (2019). *Manufacturing Processes 4-5* (Portal Book 094). Chapter 1, Unit 2, drill power feed in inches per revolution, p. 32. https://open.umn.edu/opentextbooks/textbooks/manufacturing-processes-4-5 [^virasak-tap]: Virasak, LamNgeun (2019). *Manufacturing Processes 4-5* (Portal Book 094). Chapter 1, Unit 2, power-feed tapping at 60 RPM in low gear, p. 34. https://open.umn.edu/opentextbooks/textbooks/manufacturing-processes-4-5 [^virasak-q]: Virasak, LamNgeun (2019). *Manufacturing Processes 4-5* (Portal Book 094). Chapter 1, Unit 2, unit-test questions (the 1/2-inch aluminium and 3/4-inch bronze cases), p. 35; answers derived here from Table 1, p. 30. https://open.umn.edu/opentextbooks/textbooks/manufacturing-processes-4-5 [^virasak-cnc]: Virasak, LamNgeun (2019). *Manufacturing Processes 4-5* (Portal Book 094). Chapter 8: CNC, Unit 4: CNC Language and Structure, pp. 187–200. https://open.umn.edu/opentextbooks/textbooks/manufacturing-processes-4-5 [^virasak-lathe]: Virasak, LamNgeun (2019). *Manufacturing Processes 4-5* (Portal Book 094). Chapter 2: Lathe Machine, Unit 2: Speed and Feed, pp. 65–70. https://open.umn.edu/opentextbooks/textbooks/manufacturing-processes-4-5 [^manual12]: Wikitube Microsim Guide, Sub-manual 12, Design and Manufacturing, §5.1 Spindle speed from cutting speed and §5.2 Feed per tooth and feed rate (the derived exact form 12·CS/(π·D), the 917 RPM comparison, and the pitfalls on the constant 4, the "mild steel" example, the tool material and the IPM/IPR distinction). Internal document. [^machinery]: Oberg, E.; Jones, F. D.; Horton, H. L.; Ryffel, H. H. (2012). *Machinery's Handbook*, 29th ed. New York: Industrial Press. Section on machinability and cutting speeds. Not a Portal Book; page to pin. [^taylor1907]: Taylor, F. W. (1907). "On the art of cutting metals." *Transactions of the American Society of Mechanical Engineers* 28: 31–350. (No DOI; not a Portal Book; page to pin against the journal record.) [^merchant1945]: Merchant, M. E. (1945). "Mechanics of the metal cutting process. I. Orthogonal cutting and a type 2 chip." *Journal of Applied Physics* 16 (5): 267–275. (DOI to pin; not a Portal Book.) [^kalpakjian]: Kalpakjian, S.; Schmid, S. R. (2014). *Manufacturing Engineering and Technology*, 7th ed. Upper Saddle River, New Jersey: Pearson. Chapter on the fundamentals of machining (surface roughness of a turned surface, tool life). Not a Portal Book; page to pin. ## Bibliography - Virasak, LamNgeun (2019). *Manufacturing Processes 4-5*. Open Oregon Educational Resources. Portal Book 094. https://open.umn.edu/opentextbooks/textbooks/manufacturing-processes-4-5 - Jensen, David (2024). *Introduction to Mechanical Design and Manufacturing*. Portal Book 109, Chapter 14, Manufacturing: Machining Processes, pp. 303–326 (the design-side survey of machining; not cited in the body). https://open.umn.edu/opentextbooks/textbooks/introduction-to-mechanical-design-and-manufacturing - Oberg, E. et al. (2012). *Machinery's Handbook*, 29th ed. Industrial Press. Not a Portal Book. - Kalpakjian, S.; Schmid, S. R. (2014). *Manufacturing Engineering and Technology*, 7th ed. Pearson. Not a Portal Book. ### Further reading - Taylor, F. W. (1907). "On the art of cutting metals." *Transactions of the ASME* 28. - Merchant, M. E. (1945). "Mechanics of the metal cutting process." *Journal of Applied Physics* 16. ## External links - *Manufacturing Processes 4-5* on the Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/manufacturing-processes-4-5 - For calculators and manufacturer speed-and-feed charts, see the external links of the Wikipedia pair. <!-- MATTERSIM:BEGIN g24 — Matter & Energy Cluster microsim (framework build, specs/sims/Speeds_and_feeds.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework), pending deploy:** *Speeds and feeds* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Speeds_and_feeds.html` is live. <!-- pending: <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Speeds_and_feeds.html" data-title="Speeds and feeds"></div> --> <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Speeds_and_feeds) : [Wikitube](https://en.wikitube.io/wiki/Speeds_and_feeds) · pinned revision [1369055019](https://en.wikipedia.org/w/index.php?oldid=1369055019) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Materials_science]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Materials_science row M22 · sim pending (matter/Speeds_and_feeds).*