The cutting force increased with depend on the cut and decreasing rake angle. Explain why?

A decrease of the rake angle gives increasing cutting forces. In the insert according to the invention increasing rake angle is obtained at increasing cutting depth. This means that large cutting depths cause relatively limited cutting forces, which is often of great importance. At small cutting depth, on the other hand, the cutting force problem is not as critical, but it is more essential to decrease the rake angle in order to break the chip satisfactorily. At the corner of the insert it can often be important to have particularly great chip breaking capability. By varying the extension of the corner part and the extension of the transition area between the corner and the remaining part of the cutting edge, it is possible to vary the "severity" or effect of the chip breaking.

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2.5 Approximate Calculations - use experimentally determined constants.

2.5.1 Specific Cutting Pressure The cutting force, F_c, divided by the cross section area of the undeformed chip gives the nominal cutting stress or the specific cutting pressure, p_c

NB p_c is not a true stress even though it has dimensions of stress.

2.5.2 Specific Cutting Energy The energy consumed in removing a unit volume of material is called the specific cutting energy, E₁. Energy (or work) is force F_c x distance, L, over which the force acts. The volume of material removed is V = h w L, so the specific cutting energy can be written as:

Such calculations are required to determine the size of the drive motor.

2.5.3 Material Removal Factor, K₁ is the reciprocal of the specific cutting energy and indicates the volume of material which can be removed in unit time with a drive of unit power.

These 'material constants' can not be simply used in calculations as they are not true constants but depend upon process parameters such as undeformed chip thickness, rake angle and cutting speed.

As well as energy for shearing in the primary shear zone, flank friction (between the tool flank and the newly formed surface) and friction at the cutting edge (together often referred to as the ploughing force, P) absorb energy. The energy dissipated here is almost independent of the undeformed chip thickness. When h is small a greater proportion of the energy used is absorbed here. Hence the energy required to remove a unit volume of material increases with decreasing undeformed chip thickness.

2.5.4 Adjusted Specific Cutting Energy For the above reason 'material constants', E₁ are published for agreed conditions eg: h = h_ref = 1 mm and the adjusted specific cutting energy, E, for any other h can be found from the empirical law:

where the constant 'a' ranges between 0.2 and 0.4 and may be taken as 0.3 for most materials.

For an undeformed chip thickness below 0.1 mm, the energy requirement increases even more rapidly.

2.5.5 Power Required for Cutting

The power needed by a machine tool can be estimated if the rate of material removal, V_t and m/c tool efficiency (typically in the region of 0.7 to 0.8) are known.

Power, W = E V_t/efficiency.

The table below indicates values of 'Unit Power' for for some metals, it should be noted that values vary somewhat in different sources:

Material	Hardness, BHN	Unit Power, W.s/mm3
Steel 1020	150	1.5
Steel 1040	200	1.8
Steel 1330	260	2.5
Stainless steels	135 - 275	1.4
Cast irons	110 - 190	0.8
Cast irons	190 - 320	1.6
Titanium	250 - 375	3
Super alloys (Ni and Co)	200 - 360	3 to 9
Aluminium alloys	30 - 150	0.6
Magnesium alloys	40 - 90	0.3
Copper	40	2
Leaded brass	75	0.7
Zinc alloys		0.3

2.5.6 Machinability

Machinability is not a precisely defined term, it is an attempt to account for several factors: tool life, power required for cutting, surface finish obtained, cost of removing material. The most important factor in most situations is usually tool life and machinability ratings are frequently based on this.

For many components the strength of the part is not as important as economical machining. Consequently for these applications materials are often selected for ease of machining - good tool life.

Factors that affect machinability are:
Hardness and ductility. Increasing hardness makes penetration by the tool more difficult, decreasing machinability. Generally lower ductility, which promotes discontinuous chips, is beneficial to machinability.
Because the wear of the cutting tool is heavily dependent upon the temperature it reaches, the material properties that govern this are critical:
Low workpiece: thermal conductivity, density and specific heat all give higher mean tool temperatures.
Increasing the the workpiece total cutting energy per unit volume increases the tool temperature.
So for similar tool wear rates, titanium can only be cut at about one quarter the speed of steel, which in turn can only be cut at about one tenth of the speed of aluminium.

Additions of elements such as lead, phosphorus, sulphur and tellurium to steel improves its machinability, but there are some disadvantages.

2.4 Cutting Theories

Experimentally it has been found that the shear angle and hence the cutting ratio, depend upon the workpiece and tool material and the cutting conditions. Several attempts have been made to establish a theoretical law which predicts the shear angle.

Ernst and Merchant developed the first reasonable theory. This assumed that the shear angle would take up a value to make the work done in cutting a minimum.

For given cutting conditions, the work done is proportional to F_c, an expression has been developed for F_c in terms of the shear angle and then a value for the shear angle found for which F_c is a minimum.

After some algebra this gives:

where tau is the mean angle of friction between the chip and the tool and

tau = tan^{- 1} (F/P_n)

This was later developed and other researchers have developed other expressions.

Lee and Shaffer realised that the above equation could not apply where tau = 45^o and the rake angle, alpha = 0 as these values give a shear angle, phi = 0. They considered that such conditions of high friction and low rake angle are just the conditions that lead to the formation of a built up edge. To meet this a second solution was presented where a built up edge is present on the tool face.

Experimental results show that no simple unique relationship can agree with all experimental results.

It is difficult to predict forces because the relevant flow stress is not easy to predict.

Large shear strains (1 - 5 natural strain) across a narrow zone in a very short period of time mean that strain rates are very high, several 1000 s^-1

Forces in Orthogonal Cutting

A dynamometer capable of measuring forces in 3 directions (only 2 are needed in orthogonal cutting) can be used to measure cutting forces. In the diagram below the reactions to these forces, which are acting on the tool, are shown:

F_c acting in the direction of cutting

F_t thrust force needed to keep the tool in the workpiece (direction perpendicular to the workpiece surface). At high positive rake angles the thrust force is negative and the tool is pulled into the workpiece.

The resultant force on the tool, P_r, is made up of a normal force, P_n acting perpendicular to the tool face and F the friction force acting along the face.

P_n = F_c cos(alpha) - F_t sin(alpha)

F = F_c sin(alpha) + F_t cos(alpha)

where alpha is the rake angle.

Knowledge of the shear angle, phi, will allow the deformed chip thickness to be estimated.

Idealized Chip Formation

The figure below depicts an idealized, two dimensional view of the metal cutting process. The assumptions in this model are that the tool is perfectly sharp, that the cut depth t and the cutting speed V are constant, and that the cut depth is small compared to the cut width. In this idealized model, the material layer at the top is formed into a chip by a shearing process in the primary shear zone at AB. The chip slides up the rake face undergoing some secondary plastic flow due to the forces of friction. This idealized model correctly predicts that cutting force increases with cut depth, material hardness, and friction coefficient. Cutting forces are inversely propoortional to rake angle. Power required increases with the feed rate.

Idealized Chip Formation

Built Up Edge

One important effect that is not considered in the model above is built up edge. Under most cutting conditions, some of the cut material will attach to the cutting point. This tends to cause the cut to be deeper than the tip of the cutting tool and degrades surface finish. Also, periodically the built up edge will break off and remove some of the cutting tool. Thus, tool life is reduced. In general, built up edge can be reduced by:

• Increasing cutting speed
• Decreasing feed rate
• Increasing ambient workpiece temperature
• Increasing rake angle
• Reducing friction (by applying cutting fluid)

Built Up Edge

Calculating Speeds and Feeds

Cutting speed refers to the speed at which the tool point of the cutter moves with respect to the work measured in feet per minute. Feed is the rate at which the work moves into the cutter measured in feed per tooth revolution. Feeds and speeds affect the time to finish a cut, tool life, finish of the machined surface, and power required of the machine.

The cutting speed is mostly determined by the material to be cut and the material of the tool. To find the right speed for any task, refer to the Machinery's Handbook or other reference. To calculate the proper spindle speed, divide the desired cutting speed by the circumference of the tool (or of the part if it is rotating) expressed in feet. The feed rate depends on the width and depth of cut, finish desired and many other variables. To calculate the desired feed setting from the feed rate, multiply feed per tooth per revolution by number of teeth and rpm of the spindle.

Maintained by 2.670adm@mit.edu

Most CNC milling machines or machining centers are computer controlled vertical mills with the ability to move the spindle vertically along the Z-axis. This extra degree of freedom permits their use in diesinking, engraving applications, and 2.5D surfaces such as relief sculptures. When combined with the use of conical tools or a ball nose cutter, it also significantly improves milling precision without impacting speed, providing a cost-efficient alternative to most flat-surface hand-engraving work.

CNC machines can exist in virtually any of the forms of manual machinery, like horizontal mills. The most advanced CNC milling-machines, the 5-axis machines, add two more axes in addition to the three normal axes (XYZ). Horizontal milling machines also have a C or Q axis, allowing the horizontally mounted workpiece to be rotated, essentially allowing asymmetric and eccentric turning. The fifth axis (B axis) controls the tilt of the tool itself. When all of these axes are used in conjunction with each other, extremely complicated geometries, even organic geometries such as a human head can be made with relative ease with these machines. But the skill to program such geometries is beyond that of most humans. Therefore, 5-axis milling machines are practically always programmed with CAM.

With the declining price of computers, free operating systems such as Linux, and open source CNC software, the entry price of CNC machines has plummeted. For example, Sherline, Prazi, and others make desktop CNC milling machines that are affordable by hobbyists.

Milling machine tooling

There is some degree of standardization of the tooling used with CNC Milling Machines and to a much lesser degree with manual milling machines.

CNC Milling machines will nearly always use SK (or ISO), CAT, BT or HSK tooling. SK tooling is the most common in Europe, while CAT tooling, sometimes called V-Flange Tooling, is the oldest variation and is probably still the most common in the USA. CAT tooling was invented by Caterpillar Inc. of Peoria, Illinois in order to standardize the tooling used on their machinery. CAT tooling comes in a range of sizes designated as CAT-30, CAT-40, CAT-50, etc. The number refers to the Association for Manufacturing Technology (formerly the National Machine Tool Builders Association (NMTB)) Taper size of the tool.

An improvement on CAT Tooling is BT Tooling, which looks very similar and can easily be confused with CAT tooling. Like CAT Tooling, BT Tooling comes in a range of sizes and uses the same NMTB body taper. However, BT tooling is symmetrical about the spindle axis, which CAT tooling is not. This gives BT tooling greater stability and balance at high speeds. One other subtle difference between these two toolholders is the thread used to hold the pull stud. CAT Tooling is all Imperial thread and BT Tooling is all Metric thread. Note that this affects the pull stud only, it does not affect the tool that they can hold, both types of tooling are sold to accept both Imperial and metric sized tools.

SK and HSK tooling, sometimes called "Hollow Shank Tooling", is much more common in Europe where it was invented than it is in the United States. It is claimed that HSK tooling is even better than BT Tooling at high speeds. The holding mechanism for HSK tooling is placed within the (hollow) body of the tool and, as spindle speed increases, it expands, gripping the tool more tightly with increasing spindle speed. There is no pull stud with this type of tooling.

The situation is quite different for manual milling machines — there is little standardization. Newer and larger manual machines usually use NMTB tooling. This tooling is somewhat similar to CAT tooling but requires a drawbar within the milling machine. Furthermore, there are a number of variations with NMTB tooling that make interchangeability troublesome.

Two other tool holding systems for manual machines are worthy of note: They are the R8 collet and the Morse Taper #2 collet. Bridgeport Machines of Bridgeport, Connecticut so dominated the milling machine market for such a long time that their machine "The Bridgeport" is virtually synonymous with "Manual milling machine." The bulk of the machines that Bridgeport made from about 1965 onward used an R8 collet system. Prior to that, the bulk of the machines used a Morse Taper #2 collet system.

As an historical footnote: Bridgeport is now owned by Hardinge Brothers of Elmira, New York.

Comparing vertical with horizontal

In the vertical mill the spindle axis is vertically oriented. Milling cutters are held in the spindle and rotate on its axis. The spindle can generally be extended (or the table can be raised/lowered, giving the same effect), allowing plunge cuts and drilling. There are two subcategories of vertical mills: the bedmill and the turret mill. Turret mills, like the ubiquitous Bridgeport, are generally smaller than bedmills, and are considered by some to be more versatile. In a turret mill the spindle remains stationary during cutting operations and the table is moved both perpendicular to and parallel to the spindle axis to accomplish cutting. In the bedmill, however, the table moves only perpendicular to the spindle's axis, while the spindle itself moves parallel to its own axis. Also of note is a lighter machine, called a mill-drill. It is quite popular with hobbyists, due to its small size and lower price. These are frequently of lower quality than other types of machines, however.

A horizontal mill has the same sort of x–y table, but the cutters are mounted on a horizontal arbor across the table. A majority of horizontal mills also feature a +15/-15 degree rotary table that allows milling at shallow angles. While endmills and the other types of tools available to a vertical mill may be used in a horizontal mill, their real advantage lies in arbor-mounted cutters, called side and face mills, which have a cross section rather like a circular saw, but are generally wider and smaller in diameter. Because the cutters have good support from the arbor, quite heavy cuts can be taken, enabling rapid material removal rates. These are used to mill grooves and slots. Plain mills are used to shape flat surfaces. Several cutters may be ganged together on the arbor to mill a complex shape of slots and planes. Special cutters can also cut grooves, bevels, radii, or indeed any section desired. These specialty cutters tend to be expensive. Simplex mills have one spindle, and duplex mills have two. It is also easier to cut gears on a horizontal mill.

Other milling machine variants and terminology

• Box or column mills are very basic hobbyist bench-mounted milling machines that feature a head riding up and down on a column or box way.
• Turret or vertical ram mills are more commonly referred to as Bridgeport-type milling machines. The spindle can be aligned in many different positions for a very versatile, if somewhat less rigid machine.
• Knee mill or knee-and-column mill refers to any milling machine whose x-y table rides up and down the column on a vertically adjustable knee. This includes Bridgeports.
• C-Frame mills are larger, industrial production mills. They feature a knee and fixed spindle head that is only mobile vertically. They are typically much more powerful than a turret mill, featuring a separate hydraulic motor for integral hydraulic power feeds in all directions, and a twenty to fifty horsepower motor. Backlash eliminators are almost always standard equipment. They use large NMTB 40 or 50 tooling. The tables on C-frame mills are usually 18" by 68" or larger, to allow multiple parts to be machined at the same time.
• Planer-style mills are large mills built in the same configuration as planers except with a milling spindle instead of a planing head. This term is growing dated as planers themselves are largely a thing of the past.
• Bed mill refers to any milling machine where the spindle is on a pendant that moves up and down to move the cutter into the work. These are generally more rigid than a knee mill.
• Ram type mill refers to a mill that has a swiveling cutting head mounted on a sliding ram. The spindle can be oriented either vertically or horizontally, or anywhere in between. Van Norman specialized in ram type mills through most of the 20th century, but since the advent of CNC machines ram type mills are no longer made.
• Jig borers are vertical mills that are built to bore holes, and very light slot or face milling. They are typically bed mills with a long spindle throw. The beds are more accurate, and the handwheels are graduated down to .0001" for precise hole placement.
• Horizontal boring mills are large, accurate bed horizontal mills that incorporate many features from various machine tools. They are predominantly used to create large manufacturing jigs, or to modify large, high precision parts. They have a spindle stroke of several (usually between four and six) feet, and many are equipped with a tailstock to perform very long boring operations without losing accuracy as the bore increases in depth. A typical bed would have X and Y travel, and be between three and four feet square with a rotary table or a larger rectangle without said table. The pendant usually has between four and eight feet in vertical movement. Some mills have a large (30" or more) integral facing head. Right angle rotary tables and vertical milling attachments are available to further increase productivity.
• Floor mills have a row of rotary tables, and a horizontal pendant spindle mounted on a set of tracks that runs parallel to the table row. These mills have predominantly been converted to CNC, but some can still be found (if one can even find a used machine available) under manual control. The spindle carriage moves to each individual table, performs the machining operations, and moves to the next table while the previous table is being set up for the next operation. Unlike any other kind of mill, floor mills have floor units that are entirely movable. A crane will drop massive rotary tables , X-Y tables , and the like into position for machining, allowing the largest and most complex custom milling operations to take place.
• Portical mills It has the spindle mounted in a T structure

There are many ways to classify milling machines, depending on which criteria are the focus:

Criterion	Example classification scheme	Comments
Control	Manual; Mechanically automated via cams; Digitally automated via NC/CNC	In the CNC era, a very basic distinction is manual versus CNC. Among manual machines, a worthwhile distinction is non-DRO-equipped versus DRO-equipped
Control (specifically among CNC machines)	Number of axes (e.g., 3-axis, 4-axis, or more); Within this scheme, also: Pallet-changing versus non-pallet-changing Full-auto tool-changing versus semi-auto or manual tool-changing
Spindle axis orientation	Vertical versus horizontal; Turret versus non-turret	Among vertical mills, "Bridgeport-style" is a whole class of mills inspired by the Bridgeport original
Purpose	General-purpose versus special-purpose or single-purpose
Purpose	Toolroom machine versus production machine	Overlaps with above
Purpose	"Plain" versus "universal"	A distinction whose meaning evolved over decades as technology progressed, and overlaps with other purpose classifications above; more historical interest than current
Size	Micro, mini, benchtop, standing on floor, large, very large, gigantic
Power source	Line-shaft-drive versus individual electric motor drive	Most line-shaft-drive machines, ubiquitous circa 1880-1930, have been scrapped by now
	Hand-crank-power versus electric	Hand-cranked not used in industry but suitable for hobbyist micromills

A milling machine is a machine tool used for the shaping of metal and other solid materials. Its basic form is that of a rotating cutter which rotates about the spindle axis (similar to a drill), and a table to which the workpiece is affixed. In contrast to drilling, where the drill is moved exclusively along its axis, the milling operation involves movement of the rotating cutter sideways as well as 'in and out'. The cutter and workpiece move relative to each other, generating a toolpath along which material is removed. The movement is precisely controlled, usually with slides and leadscrews or analogous technology. Often the movement is achieved by moving the table while the cutter rotates in one place, but regardless of how the parts of the machine slide, the result that matters is the relative motion between cutter and workpiece. Milling machines may be manually operated, mechanically automated, or digitally automated via CNC (computer numerical control).

Milling machines can perform a vast number of operations, some of them with quite complex toolpaths, such as slot cutting, planing, drilling, diesinking, rebating, routing, etc.

Cutting fluid is often pumped to the cutting site to cool and lubricate the cut, and to sluice away the resulting swarf.