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

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:

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.

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.