Hello friends, Today we will Discuss about the Taylor’s tool life equation derivation.
What is Tool Life?
 Tool life is actual working period of fresh cutting tool which gives satisfactory work & after that it needs to resharpen or replace.
 Hence it is period from when the fresh tool starts work till it needs to replace or resharpen.
 The tool life can be expressed as,
 Working period in minutes.
 Number of jobs to machined.
 Volume of material removal.
 Total length of cutting.
 The factor which influence tool life are,
 Cutting velocity
 depth of cut
 Feed rate
Out of them cutting velocity affects the tool life to higher extent.
Taylor’s equation for tool life:
The following graph shows the relation between cutting velocity (`V_{C}`) & rate of tool wear.
When the cutting velocity is slower the tool wear is slower which leads to higher tool life.
And as cutting velocity increases the rate of tool wear increase which results in lower tool life.
When other factors like depth of cut, feed rate are not considered, then taylor’s equation for tool life is written as,
`VT^{n}=C`
Where
 V = Cutting velocity
 T = Time in minutes
 n = Tool life exponent
Modified taylor’s equation for tool life:
In taylor’s tool life equation, only cutting velocity is considered to find tool life. But in actual feed rate (`S_{o}`), depth of cut (t) also affect the tool life.
By considering all affecting factor modified taylor’s equation for tool life is written as,
`T=frac{C_{T}}{V_{c}^{x}times S_{o}^{y}times t^{z}}`
Where,
 T = Tool life in minute
 `V_{o}` = Cutting velocity
 `S_{o}` = Feed rate
 t = Depth of cut
Where terms `C_{T}`, x, y, z are depend on tool & job material which can found in machining data handbook.
FAQ’s:

What is the tool life equation and state the factor affecting the tool life?
Tool life equation is `VT^{n}=C`
The factor affecting the tool life are Cutting velocity, depth of cut, Feed rate. 
How is tool life calculated? / How is cutting tool life calculated?
Using modified taylor’s equation for tool life, we can calculate tool life in minutes.
`T=frac{C_{T}}{V_{c}^{x}times S_{o}^{y}times t^{z}}`