For all metal-cutting processes, "speeds and feeds" are important parameters. The colloquial term "speeds and feeds" refers to the speed, feed, and depth of cut of a metal-cutting process. To describe these parameters, we will be using the turning process. The figure below shows the important geometry. The speed (Labeled on the figure as V.) is the cutting speed, which is a measure of the part cut surface speed relative to the (here, stationary) tool.

Speed is a velocity unit, which is typically listed in terms of feet/min, inches/min, meters/second, or meters/min.

Feed (Labeled on the figure as f_r), is the amount of material removed for each revolution or per pass of the tool over the workpiece. Feed is measured in units of length/revolution, length/pass, length/tooth, length/time, or other appropriate unit for the particular process.

The depth of cut, DOC (Labeled on the figure as d.), represents the third parameter for metal cutting. For turning, DOC is the depth that the tool is plunged into the surface. The DOC is half of the difference in the diameters D_a and D_b,

the initial and final diameters, respectively.





Below is a summary list of the terms used.






Speeds and feeds are important since they are critical input parameters which determine the output of a machine tool. Other inputs include the material of the part, the shape of the raw stock and final part, and the geometry of the machine tool used. Outputs include the surface finish, the time to machine each part, the temperature of the cutting tool and cut part, the residual stresses left in the part, and warping of the part.

Speeds and feeds typically take much experience and experimenation to determine accurately, but a good place to start is a table of recommended speeds and feeds. The MRR, or the Metal Removal Rate, is listed at the end of the above relation list. For turning, MRR values range from 0.1 to 600 in³ per minute. Most processes have MRR's that can be expressed as the volume of metal removed divided by the time needed to remove it:
MRR = (volume of cut)/(cutting time).
MRR can be used to estimate the power required to sustain the cutting operation. With turning, the cutting time can be expressed as the following:



Where the symbols have the same meanings as defined earlier on this page and the allowance is an estimation factor which is added to the L term to allow for the tool to enter and exit the cut.


A single-point tool is a cutting tool that cuts only at a single edge or area of the cutting tool. Turning and shaping are examples of single-point cutting. Multiple-point cutting processes are milling and drilling.

For efficient cutting a tool must have the following properties:

Hot Hardness

This means the ability to retain its hardness at high temperatures. All cutting operations generate heat, which will affect the tool¡¦s hardness and eventually its ability to cut.

Strength and Resistance to Shock

At the start of a cut the first bite of the tool into the work results in considerable shock loading on the tool. It must obviously be strong enough to withstand it.

Low Coefficient of Friction

The tool rubbing against the workpiece and the chip rubbing on the top face of the tool produce heat which must be kept to a minimum

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.