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Recommended Reading:

 Manufacturing Engineering and Technology

  Machinery's Handbook

  Marks' Standard Handbook for Mechanical Engineers

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TAYLOR’S EQUATION. (VTⁿ = C)

The following is an example of how Taylor’s equation sometimes referred to as ‘Taylor’s tool life theory’ may be used to compare percentage change in tool life at different cutting speeds. For the purpose of comparison cutting speed (V, in this instance) may be expressed linearly or as a spindle speed, providing the same units of measurement are used for both cutting speeds to be compared i.e. m/min OR rev./min.

The value of index (n) for most combinations of tool and work piece material can be found in table form in good machining handbooks.

The value of constant (C) may be determined by calculation after observing (and measuring) the particular setup. Note: absolute values of tool life (T) and constant (C) are not required for calculating percentage tool life change.

Example:

A lathe running at a speed of 4000 rev./min is cutting Mild Steel with a H.S.S. tool. The spindle speed is reduced to 3000 rev./min. calculate the percentage change in tool life.

V₁ = Initial cutting speed. V₂ = Reduced cutting speed.

T₁ = Tool life at V₁. T₂ = Tool life at V_2.

n = 0.125

VTⁿ = C

VT^0.125 = C

So T₁^0.125 = C

                     V₁

And T₂^0.125 = C

                 V₂

(T₁/T₂)^0.125 = (C/V₂)

                        (C/V₁)

(T₂/T₁)^0.125 = C   x   V₁

                      V₂      C

(T₂/T₁)^0.125 = V₁

                       V₂

(T₂/T₁) = 9.99

T₂ = 9.99xT₁

This shows that reducing cutting speed by 25% increases tool life by nearly 1000% (under the cutting conditions of this particular setup).

The tool life (T) is determined by observation, the value of constant (C) may then be determined for the particular setup.

In the previous example, for instance, if it were to be observed that the initial tool life (T₁) was 4 hours and cutting speed 30m/min., then: -

VTⁿ = C

30 x (4x60_(mins))^0.125

C = 59.5

Calculations may now be carried out to ascertain tool life if a different tool material, e.g. Carbide, is used; simply using the relevant value of n.

EXAMPLE

If the value of n for mild steel workpiece material and carbide tool material is 0.1 then at the same cutting speed of 30 m/min: -

VTⁿ = C

30 x T^0.1 = 59.5

T^0.1 = 59.5

         30

T = 941 minutes

As opposed to 240 minutes using the H.S.S. tool.

    Suggested Reading:

  Handbook of Mechanical Engineering Calculations

Whilst every effort has been made to ensure the accuracy of this site the author can accept no responsibility for any loss, harm or damage howsoever caused by the use of the content of this site.