Cutting Speed, Feed and Tool Life: Unit Checks Across the Full Calculation Chain

Publish time 10/24/2026Author ToSea Technical Editorial TeamSource brother.cn

From cutting speed to spindle speed, feed per tooth, material removal rate and tool life, a continuous worked example illustrates the relationships among common machining parameters and how to convert their units.

Machining parameters are often passed between different spreadsheets and people. Even when a number is copied correctly, it can lose its original meaning because of differences in units, diameter definitions or feed basis. This article links several common quantities into a calculation chain that can be independently recomputed, focusing on checking the relationships among these quantities. The values in the text are teaching examples only, not universal cutting parameters for any particular material.

Cutting speed describes circular motion

Cutting speed is the surface linear speed of the cutting edge relative to the workpiece. When turning a cylindrical outer diameter, the workpiece diameter at the machined location is usually used; when milling, the cutting diameter at the relevant depth of cut is used. You cannot assume that two tools of different diameters have the same cutting speed just because the spindle speed shown on the machine screen is the same. For ball-nose and large-radius tools, the effective diameter should also be determined first.

v_c=\frac{\pi D n}{1000}

Metric cutting speed: diameter in millimeters, spindle speed in revolutions per minute, and the result in meters per minute.

Take a diameter of 10 mm and a spindle speed of 500 r/min; the circumference of one revolution is the diameter multiplied by pi, and the distance traveled in one minute is that circumference multiplied by the spindle speed. Converted to meters, this gives approximately 15.708 m/min. If the diameter is halved while the spindle speed stays the same, the linear speed is also halved. This proportional relationship can be used directly to check whether a spreadsheet entry has an order-of-magnitude error.

D=10\,\mathrm{mm},\quad n=500\,\mathrm{rpm},\quad v_c\approx15.708\,\mathrm{m/min}

An independent speed example; all numbers can be recomputed using the relationship above.

D=5\,\mathrm{mm},\quad n=500\,\mathrm{rpm},\quad v_c\approx7.854\,\mathrm{m/min}

Reference speed when the diameter is halved and the spindle speed is unchanged.

n=\frac{1000v_c}{\pi D}

When back-calculating spindle speed, the denominator contains the product of pi and the diameter.

Before back-calculating speed, you must first check the speed unit. If the input is m/s, first multiply by 60 to convert it to m/min, then enter the current metric formula. Mixing seconds and minutes causes a 60-fold difference; mixing millimeters and meters for the diameter causes another 1000-fold difference. Before substituting values, confirm that the units are consistent with the time and length bases used by the formula.

Feed rate describes movement along the path

Feed rate and cutting speed are two different physical quantities. The former describes the distance the tool moves per minute along the machining path or in the direction of the worktable, while the latter describes the circumferential linear speed at the point where the cutting edge contacts the workpiece. Increasing one of these quantities does not mean the other automatically changes in the same proportion. When discussing machining time, it is also necessary to distinguish the actual cutting travel, air moves, acceleration and deceleration, and non-cutting time such as tool changes.

v_f=f_z z n

Milling feed rate equals the product of the feed per tooth, the effective number of teeth used to calculate the feed, and the spindle speed.

The number of teeth here must be consistent with the definition in the tool formula being used; the instantaneous number of teeth in contact with the workpiece at the same time should not be freely interchanged with the number of teeth used to calculate the feed in the catalog.

f_z=0.08\,\mathrm{mm},\quad z=4,\quad n=6000\,\mathrm{rpm},\quad v_f=1920\,\mathrm{mm/min}

Substituting the feed per tooth, the calculated number of teeth, and the speed into the formula gives the worktable feed rate.

f_z=\frac{v_f}{zn},\qquad f_n=\frac{v_f}{n}

Feed per tooth differs from feed per revolution: one is distributed per tooth, while the other is calculated per spindle revolution.

Back-calculating from the previous example gives the feed per revolution, which is then divided by the number of tool teeth to obtain the feed per tooth. Single-edge tools in turning often use feed per revolution directly; when discussing feed per tooth in milling, the number of teeth must be clearly specified. Mixing up the translations of these two terms in a given language will cause an article that appears formally complete to still convey incorrect machining conditions.

f_n=0.32\,\mathrm{mm/rev},\qquad f_z=0.08\,\mathrm{mm}

Continuing with the feed per revolution and feed per tooth back-calculated in the previous example.

Physical quantity	Symbol	Example	Unit
Cutting diameter	D	10	mm
Spindle speed	n	6000	rpm
Feed per tooth	f_z	0.08	mm
Number of teeth used for feed calculation	z	4	1
Table feed rate	v_f	1920	mm/min
Feed per revolution	f_n	0.32	mm/rev

Cubic unit for material removal rate

Q=\frac{a_p a_e v_f}{1000}

Axial depth of cut and radial width of cut are both in millimeters, feed is in millimeters per minute, and the volumetric removal rate is converted to cubic centimeters per minute.

If the axial depth of cut and radial width of cut are both 2 mm, and the feed rate from the previous example is used, then 7,680 mm³ is removed per minute, which is 7.68 cm³. The denominator 1,000 comes from the conversion from cubic millimeters to cubic centimeters. Just because 10 is common in length unit conversions, do not change the volume conversion here to dividing by 10.

a_p=2\,\mathrm{mm},\quad a_e=2\,\mathrm{mm},\quad v_f=1920\,\mathrm{mm/min},\quad Q=7.68\,\mathrm{cm^3/min}

Material removal rate calculated from the axial depth of cut, radial width of cut and feed rate.

Typesetting check: the volume unit is cm³/min; the speed unit may be written as min⁻¹; the subscript in the variable is v_c. Superscripts and subscripts distinguish different physical quantities; when reading parameters, each should be matched item by item against the variable definitions.

The tool life exponent must be kept separate from the spindle speed

v_cT^p=C,\qquad \frac{T_2}{T_1}=\left(\frac{v_{c1}}{v_{c2}}\right)^{1/p}

Simplified tool life relationship: independent symbols are used for the exponent, and the constant is only comparable when the applicable conditions remain unchanged.

To avoid symbol conflicts, this article uses independent symbols to represent the empirical life exponent, and uses n to denote the spindle speed. For mathematical demonstration purposes only, increasing the cutting speed to 110 % of the original yields a life ratio of approximately 0.683. This result depends on the assumed empirical exponent and unchanged conditions; it does not imply that all tools will necessarily follow the same ratio after a speed increase.

p=0.25,\quad v_{c2}=1.1v_{c1},\quad T_2/T_1\approx0.683

A mathematical demonstration of the exponent, speed ratio, and life ratio yields an approximate result.

Actual machining may encounter different limitations such as wear, chipping, vibration, or thermal deformation. Empirical life formulas cannot reliably predict random chipping, nor can they replace the recommendations provided by tool manufacturers for specific materials, coatings, cooling, and tool geometry. Calculation results must be used together with the applicable working conditions and constraints.

Establishing verifiable parameter handover

It is recommended to record the physical quantity name, symbol, numerical value, unit, and calculation basis together on a single process sheet. During review, first check the diameter value, then the time base and length units, and finally back-calculate the feed and material removal rate. When an abnormal order of magnitude is found, one should return to the input conditions rather than merely adjusting the final result to make it appear reasonable.

When selecting machining parameters, one should simultaneously verify the input values, units, variable definitions, and applicable working conditions. Each step in the calculation chain should use consistent time and length bases to avoid directly comparing results from different machining conditions.

This article is a recalculated case study based on publicly available technical data. The examples facilitate independent checking of arithmetic, units, subscripts/superscripts, and professional terminology; actual production must still rely on machine tool capabilities, tool catalogs, trial cut records, and approved process documentation.

Source note: This article was originally written based on the public technical materials listed, and the calculation examples have been independently recalculated.

Brother machine tools: cutting speed topic: https://www.brother.cn/machinetool/speedio-navi/articles/a0048/index

Sandvik Coromant: milling definitions and formulas: https://www.sandvik.coromant.com/en-gb/knowledge/machining-formulas-definitions/milling-formulas-definitions