A line drawing showing some basic concepts of speeds and feeds in the context of lathe work. The angular velocity of the workpiece (rev/min) is called the “spindle speed” by machinists. Its tangential linear equivalent at the workpiece surface is called the “cutting speed”, “surface speed”, or simply the “speed” by machinists. The “feeds” may be for the X-axis or the Z-axis (typically mm/rev or inch/rev for lathe work; sometimes measured as mm/min or inch/min). Notice that as the tool plunges closer to the workpiece’s center, the same spindle speed will yield a decreasing surface (cutting) speed (because each rev represents a smaller circumfrance distance, but takes the same amount of time). Most cnc lathes have constant surface feed to counteract that natural decrease, which speeds up the spindle as the tool plunges in.

Milling cutter paused after taking a cut. Arrows show the vectors of various velocities collectively known as speeds and feeds. The circular arrow represents the angular velocity of the spindle (rev/min), called the “spindle speed” by machinists. The tangential arrow represents the tangential linear velocity at the outer diameter of the cutter, called the “cutting speed”, “surface speed”, or simply the “speed” by machinists. The arrow colinear with the slot that has been milled represents the linear velocity at which the cutter is advanced laterally . This velocity is called the “feed” by machinists.

The phrase speeds and feeds or feeds and speeds refers to two separate velocities in machine tool practice, cutting speed and feed rate. They are often considered as a pair because of their combined effect on the cutting process. Each, however, can also be considered and analyzed in its own right.

Cutting speed  is the speed difference between the cutting tool and the surface of the workpiece it is operating on. It is expressed in units of distance across the workpiece surface per unit of time, typically surface feey per minute  or meters  per minute   Feed rate is the relative velocity at which the cutter is advanced along the workpiece; its vector is perpendicular  to the vector of cutting speed. Feed rate units depend on the motion of the tool and workpiece; when the workpiece rotates , the units are almost always distance per spindle revolution (inches per revolution [in/rev or ipr] or millimeters per revolution . When the workpiece does not rotate , the units are typically distance per time (inches per minute or millimeters per minute , although distance per revolution or per cutter tooth are also sometimes used.

Cutting speed

Cutting speed may be defined as the rate at the workpiece surface, irrespective of the machining operation used. A cutting speed for mild steel of 100 ft/min is the same whether it is the speed of the cutter passing over the workpiece, such as in a turning operation, or the speed of the cutter moving past a workpiece, such as in a milling operation. The cutting conditions will affect the value of this surface speed for mild steel.

Schematically, speed at the workpiece surface can be thought of as the tangetial  speed at the tool-cutter interface, that is, how fast the material moves past the cutting edge of the tool, although “which surface to focus on” is a topic with several valid answers. In drilling and milling, the outside diameter of the tool is the widely agreed surface. In turning and boring, the surface can be defined on either side of the depth of cut, that is, either the starting surface or the ending surface, with neither definition being “wrong” as long as the people involved understand the difference. An experienced machinist summed this up succinctly as “the diameter I am turning from” versus “the diameter I am turning to.” He uses the “from”, not the “to”, and explains why, while acknowledging that some others do not. The logic of focusing on the largest diameter involved (OD of drill or end mill, starting diameter of turned workpiece) is that this is where the highest tangential speed is, with the most heat generation, which is the main driver of tool wear

There will be an optimum cutting speed for each material and set of machining conditions, and the spindle speed can be calculated from this speed. Factors affecting the calculation of cutting speed are:

• The material being machined (steel, brass, tool steel, plastic, wood) (see table below)
• The material the cutter is made from High carbon steel ,hisg speed steel, Carbide, Ceramic , and Diamond tools
• The economical life of the cutter (the cost to regrind or purchase new, compared to the quantity of parts produced)

Cutting speeds are calculated on the assumption that optimum cutting conditions exist. These include:

• Metal removal rate
• Full and constant flow of cutting fluid  
• Rigidity of the machine and tooling setup
• Continuity of cut
• Condition of material

The cutting speed is given as a set of constants that are available from the material manufacturer or supplier. The most common materials are available in reference books or charts, but will always be subject to adjustment depending on the cutting conditions. The following table gives the cutting speeds for a selection of common materials under one set of conditions. The conditions are a tool life of 1 hour, dry cutting (no coolant), and at medium feeds, so they may appear to be incorrect depending on circumstances. These cutting speeds may change if, for instance, adequate coolant is available or an improved grade of HSS is used (such as one that includes [cobalt]).

Spindle speed

The spindle speed is the rotational frequency of the spindle of the machine, measured in revolutions per minute (RPM). The preferred speed is determined by working backward from the desired surface speed (sfm or m/min) and incorporating the diameter (of workpiece or cutter).

Excessive spindle speed will cause premature tool wear, breakages, and can cause tool chatter, all of which can lead to potentially dangerous conditions. Using the correct spindle speed for the material and tools will greatly enhance tool life and the quality of the surface finish.

Grinding wheels are designed to be run at a maximum safe speed, the spindle speed of the grinding machine may be variable but this should only be changed with due attention to the safe working speed of the wheel. As a wheel wears it will decrease in diameter, and its effective cutting speed will be reduced. Some grinders have the provision to increase the spindle speed, which corrects for this loss of cutting ability; however, increasing the speed beyond the wheels rating will destroy the wheel and create a serious hazard to life and limb.

Spindle speed becomes important in the operation of routers, spindle moulders or shapers, and drills. Older and smaller routers often rotate at a fixed spindle speed, usually between 20,000 and 25,000 rpm. While these speeds are fine for small router bits, using larger bits, say more than 1-inch (25 mm) or 25 millimeters in diameter, can be dangerous and can lead to chatter. Larger routers now have variable speeds and larger bits require slower speed. drilling goods  generally uses higher spindle speeds than metal, and the speed is not as critical. However, larger diameter drill bits do require slower speeds to avoid burning.

Cutting feeds and speeds, and the spindle speeds that are derived from them, are the ideal cutting conditions for a tool. If the conditions are less than ideal then adjustments are made to the spindle’s speed, this adjustment is usually a reduction in RPM to the closest available speed, or one that is deemed to be correct.

Spindle speed calculations

Most metalworking books have nomograms or tables of spindle speeds and feed rates for different cutters and workpiece materials; similar tables are also likely available from the manufacturer of the cutter used.

The spindle speeds may be calculated for all machining operations once the SFM or MPM is known. In most cases, we are dealing with a cylindrical object such as a milling cutter or a workpiece turning in a lathe so we need to determine the speed at the periphery of this round object. This speed at the periphery (of a point on the circumference, moving past a stationary point) will depend on the rotational speed (RPM) and diameter of the object.

The following formulae may be used to estimate this value.

Approximation

The exact RPM is not always needed, a close approximation will work (using 3 for the value of {\displaystyle {\pi }}).{\displaystyle RPM={CuttingSpeed\times 12 \over \pi \times Diameter}}

e.g. for a cutting speed of 100 ft/min (a plain HSS steel cutter on mild steel) and diameter of 10 inches (the cutter or the work piece){\displaystyle RPM={CuttingSpeed\times 12 \over \pi \times Diameter}={12\times 100ft/min \over 3\times 10inches}={40revs/min}}

and, for an example using metric values, where the cutting speed is 30 m/min and a diameter of 10 mm (0.01 m),{\displaystyle RPM={Speed \over \pi \times Diameter}={1000\times 30m/min \over 3\times 10mm}={1000revs/min}}

Accuracy

However, for more accurate calculations, and at the expense of simplicity, this formula can be used:{\displaystyle RPM={Speed \over Circumference}={Speed \over \pi \times Diameter}}

and using the same example{\displaystyle RPM={100ft/min \over \pi \times 10\,inches\left({\frac {1ft}{12\,inches}}\right)}={100 \over 2.62}=38.2revs/min}

and using the same example as above{\displaystyle RPM={30m/min \over \pi \times 10\,mm\left({\frac {1m}{1000\,mm}}\right)}={1000*30 \over \pi *10}=955revs/min}

where:

• RPM is the rotational speed of the cutter or workpiece.
• Speed is the recommended cutting speed of the material in meters/minute or feet/min
• Diameter in millimeters or inches.

Feed rate

Feed rate is the velocity at which the cutter is fed, that is, advanced against the workpiece. It is expressed in units of distance per revolution for turning and boring (typically inches per revolution [ipr] or millimeters per revolution). It can be expressed thus for milling also, but it is often expressed in units of distance per time for milling (typically inches per minute [ipm] or millimeters per minute), with considerations of how many teeth (or flutes) the cutter has then determined what that means for each tooth.

Feed rate is dependent on the:

• Type of tool (a small drill or a large drill, high speed or carbide, a boxtool or recess, a thin form tool or wide form tool, a slide knurl or a turret straddle knurl).
• Surface finish desired.
• Power available at the spindle
• Rigidity of the machine and tooling setup
• Strength of the workpiece
• Characteristics of the material being cut, chip flow depends on material type and feed rate. The ideal chip shape is small and breaks free early, carrying heat away from the tool and work.
• Threads per inch  (TPI) for taps, die heads and threading tools.
• Cut Width. Any time the width of cut is less than half the diameter, a geometric phenomenon called Chip Thinning reduces the actual chipload. Feedrates need to be increased to offset the effects of chip thinning, both for productivity and to avoid rubbing which reduces tool life.

When deciding what feed rate to use for a certain cutting operation, the calculation is fairly straightforward for single-point cutting tools, because all of the cutting work is done at one poi. With a milling machine or jointer, where multi-tipped/multi-fluted cutting tools are involved, then the desired feed rate becomes dependent on the number of teeth on the cutter, as well as the desired amount of material per tooth to cut .The greater the number of cutting edges, the higher the feed rate permissible: for a cutting edge to work efficiently it must remove sufficient material to cut rather than rub; it also must do its fair share of work.

Formula to determine feed rate

This formula can be used to figure out the feed rate that the cutter travels into or around the work. This would apply to cutters on a milling machine, drill press and a number of other machine tools. This is not to be used on the lathe for turning operations, as the feed rate on a lathe is given as feed per revolution.

{\displaystyle FR={RPM\times T\times CL}}

Where:

• FR = the calculated feed rate in inches per minute or mm per minute.
• RPM = is the calculated speed for the cutter.
• T = Number of teeth on the cutter.
• CL = The chip load or feed per tooth. This is the size of chip that each tooth of the cutter takes.

Depth of cut

Cutting speed and feed rate come together with depth of cut to determine the material removal rate , which is the volume of workpiece material (metal, wood, plastic, etc.) that can be removed per time unit.

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