Economics of Metal Removal

Economics of Metal Removal

Economics of Metal Removal - When a manufacturing process consists of removing metal with a single point tool, the type of tool used or cutting speed chosen can have an effect upon the total cost of the product. It is worth considering this because the removal of metal in this manner is still a major process in the engineering industry.

In a roughing operation the object is to remove a certain volume of material at minimum cost or minimum time or maximum profit, and the type of tool and cutting speed should be chosen accordingly. In a finishing operation the object is to improve a certain area of material until it is of the desired quality of finish. In the following discussion the chosen criterion is the removal of certain volume of material at minimum cost.

Again it should be emphasized that the analysis used to obtain the optimum conditions is worthless unless the cost information used is relatively accurate.

F. W. Taylor introduced the well known relationship between the cutting speed used in a metal removing operation and the life of the tool, viz.,

VTⁿ= C

where V = cutting speed

T = tool life

(Although in basic SI units meters and seconds should be used, metres and minutes are the practical units)

n = an index closely related to the cutting tool material, and the following values may be used:

0.1 to 0.15 for high speed steel tools

0.2 to 0.4 for tungsten carbide tools

0.4 to 0.6 for ceramic tools

C = a constant

This is an empirical relationship and for any given set of cutting conditions over a practical range of speeds, it can be considered valid. If the cutting conditions are changed however, (i.e., feed, depth of cut, rake angle, tool shape, workpiece material etc.) then the relationship will cease to be true. It can be seen then that for a particular machining operation all the variables, other than V and T, must be kept constant otherwise the law is not valid.

The curve is exponential. Cutting tests must be used to obtain values of n and C. These values are difficult to obtain accurately, because in turn it is difficult to assess when the effective cutting life of the tool has ceased during the test. As a tool is tested with varying cutting speeds, a sensible criterion must be adopted to determine tool life. Then the values obtained for V and T from the test with controlled cutting conditions can be plotted on a graph, using a log log scale.

The slope of the straight line will give the value of n, and hence a value for C can be obtained.

It can be seen that if cutting speed V is increased, then tool life T will decrease. Hence, metal is removed faster and therefore more cheaply. But tool life is shorter and therefore tools replacement and servicing are more costly.

V_T= Optimum cutting speed where the total cost of machining a batch of components y is at a minimum.

In order to find an expression for V_T the tooling cost and metal removal cost (or machining cost) must be added to give the total cost. Then by calculus the turning point of the curve and hence V_E can be found.

Let H = machining cost/minute i.e., labour cost/minute + over­ heads/minute.

Let J = tooling cost i.e., cost of changing tool + cost of regrinding + tool depreciation.

Let Y₁ = cost of machining metal/unit volume of metal cut.

Let Y₂ = cost of servicing/tools volume of metal cut.

Let Y=total cost/unit volume of metal cut = Y₁ + Y₂

=1/dfV

Where d=depth of out

f =feed in length/rev

V=cutting speed

This expression will enable V_T be calculated so that the optimum cutting speed can be found to give minimum cost Y_T for the batch. It should be noticed that n from Taylor's equation is important in this equation, hence the need to obtain its value accurately. In this analysis we have not included the costs of handling the tool.