# Understanding cutting equations

Surface feet per minute, chip load, undeformed chip thickness and check cutting are companion shop terms. Over the final few weeks, however, several occurrences in our shop have made me realize there are a draw of metalworking professionals who don ’ t understand these terms and the calculations that go along with them. Whether you work at a little job shop or a large compress manufacturer, it is crucial to understand cutting tool calculations and how to use them to help drive significant efficiency gains .
Cutting travel rapidly calculations might well be the most important ones. They are easy to use and, with a little explanation, easy to understand. The cutting speed of a tool is expressed in surface feet per minute ( sfm ) or airfoil meters per minute ( m/min. ). alike to mph for a car, sfm is the linear outdistance a cutting joyride travels per minute. To get a better sense of plate, 300 sfm, for exercise, converts to 3.4 miles per hour .
Toolmakers recommend cutting speeds for different types of workpiece materials. When a toolmaker suggests 100 sfm, it is indicating the outside come on of the rotating joyride should travel at a pace of travel rapidly equal to 100 linear feet per moment. If the creature has a circumference ( diameter × π ) of 12 ”, it would need to rotate at 100 revolutions per minute to achieve 100 sfm .
All images courtesy C. Tate

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Imagine the cutting cock as a rolling ring or cylinder. The distance traveled in one rotation times rpm is its surface rush. If the circle above had a diameter of 3.82 ”, the circumference would be 12 ”. As a solution, every revolution would produce a linear distance of 1 ‘, and a spindle speed of 100 rpm would be a cutting speed of 100 sfm .
The watch equality is used to calculate spike rush : revolutions per minute = sfm ÷ diameter × 3.82, where diameter is the cutting creature diameter or the share diameter on a lathe in inches, and 3.82 is a constant that comes from an algebraic simplifica-tion of the more complex convention : revolutions per minute = ( sfm × 12 ) ÷ ( diameter × π ) .
Because the tool diameter is measured in inches, the “ feet ” in sfm must be converted to inches, and because there are 12 inches in a metrical foot, breed sfm by 12. In addition, the circumference of the creature is found by multiplying the instrument diameter by π, or 3.14 to simplify. The solution is : revolutions per minute = ( sfm × 12 ) ÷ ( diameter × π ) = ( sfm ÷ diameter ) × ( 12 ÷ π ) = ( sfm ÷ diameter ) × 3.82 .
Notice the vertical lines, called tool marks, on the outside of the separate being turned. As the feed rate increases, the distance between the lines besides increases. The chip thickness is approximately equal to the feed .
Cutting speeds are published in sfm because the ideal cutting accelerate for a particular syndicate of tools will, in hypothesis, be the same no count the size of the joyride. The engineer, programmer or machinist is expected to calculate the revolutions per minute needed to produce the proper cutting speed for each selected joyride .
indeed what is this telling us ? Let ’ s say a 1 ” -dia. creature must run at 100 sfm. Based on the equality, that tool must turn at 382 revolutions per minute to achieve 100 sfm : 100 ÷ 1 × 3.82 = 382 .
Another way to consider this concept is to think about the distance the 1 ” creature would travel were it to make 382 revolutions across the patronize floor. In that scenario, it would travel 100 ‘ ; do it in 60 seconds and it would be traveling 100 sfm.

Lathes are different, of class, because the workpiece rotates alternatively of the tender. Because the formula for cutting accelerate is dependant on diameter, as the diameter of the workpiece decreases, rpm must increase to maintain a constant surface rush. After each circular cut on the lathe, the workpiece OD decreases or the ID increases, and it is necessary for the revolutions per minute of the contribution to increase to maintain the craved cutting accelerate. As a leave, CNC manufacturers developed the changeless surface footage feature for lathe controls. This feature allows the programmer to input the desire cutting focal ratio in sfm or m/min. and the see calculates the proper revolutions per minute for the transfer diameter .
While the instrument or separate is spinning, the machine must know how fast to travel while the stonecutter is engaged in the workpiece. fertilize rate is the term that describes the traverse rate while cutting .
feed rate for mill is normally expressed in inches per hour ( ipm ) and calculated using : ipm = revolutions per minute × no. of flutes × chip cargo .
What is chip cargo ? When mill, it is the amount of material that the cutting edge removes each prison term it rotates. When turning, it is the distance the function moves in one revolution while engaged with the creature. It is sometimes referred to as chip thickness, which is sort of on-key. Chip thickness can change when early parameters like radial DOC or the creature ’ s go angle variety .
Toolmakers print chip load recommendations along with cutting travel rapidly recommendations and express them in thousandths of an edge ( millimeter for metric unit units ). For mill and boring operations, chip load is expressed in thousandths of an inch per flute. Flutes, teeth and cutting edges all describe the like thing and there must be at least one, but, in theory, there is no limit to the number a cock can have .
Chip burden recommendations for turning operations are most frequently given in thousandths of an inch per revolution, or feed per rev up. This is the outdistance the tool advances each time the region com-pletes one rotation .
What revolutions per minute and fertilize rate should be programmed for a 4-flute, 1 ” endmill, running at a recommend cutting travel rapidly of 350 sfm and a commend chip load of 0.005 edge per tooth ( ipt ) ? Using the equation, rpm = sfm ÷ diameter × 3.82 = 350 ÷ 1.0 × 3.82 = 1,337, the tip rate = revolutions per minute × no. of flutes × chip load = 1,337 × 4 × 0.005 = 26.74 ipm.

here is where things get interest, because by changing the values in the convention, the relationships of the different variables become discernible. Try applying a 2 ” tool rather of the 1 ” tool. What happens ? The revolutions per minute and feed rate decrease by half .
Understanding these relationships and applying some creative remember can provide significant gains in efficiency. I will discuss how to take advantage of these relationships in my next column. CTE
About the generator : Christopher Tate is aged advance manufacture engineer for Milwaukee Electric Tool Corp., Brookfield, Wis. He is based at the company ’ s fabricate plant in Jackson, Miss. He has 19 years of experience in the metalworking industry and holds a master of Science and Bachelor of Science from Mississippi State University. e-mail : chris23tate @ gmail.com .

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