Solving extended Taylor for tool life estimation in machining

Hi, Im trying to make a script for easy calculations of tool life using extended Taylor method by solving a system of equations of the form

C*(V^A)*(f^B)*(ap^D)*(VB^E) = T

where V,f,ap,VB and T are numerical values and C, A, B, D, E are constants

How would one go about writing a function for calculating this? Any help or pointers are greatly appreciated!

Best regards, //Henrik

[Keith Hooks]

How would you like to pass the variables and constants? Do you want to hardcode the constants inside the function?

Answer 1

[John D'Errico]

The simple answer? Don't. Instead, do it the easy way, the trivial way.

If you have

C*(V^A)*(f^B)*(ap^D)*(VB^E) = T

then it is equally true that

log(C ) + A*log(V) + B*log(f) + D*log(ap) + E*log(VB) = log(T)

If we now transform C (since it is an unknown constant) so that

Chat = log(C )

then we see that you have a linear system for the unknowns {A,B,Chat,D,E}

log(C ) + A*log(V) + B*log(f) + D*log(ap) + E*log(VB) = log(T)

Use backslash to solve the now linear system of equations.