How can `tan lambda = (cos phi_n*tan lambda- mu)/(cos phi_n + mu*tan lambda)` be proved. I have a relation for back drive efficiency given by `e_b = (1/tan lambda)*(cos phi_n*tan lambda- mu)/(cos...

How can `tan lambda = (cos phi_n*tan lambda- mu)/(cos phi_n + mu*tan lambda)` be proved. I have a relation for back drive efficiency given by `e_b = (1/tan lambda)*(cos phi_n*tan lambda- mu)/(cos phi_n + mu*tan lambda)`

 

Refer the equation 11 for lead angle back drive efficiency at:

http://roton.com/formulas.aspx

Expert Answers
justaguide eNotes educator| Certified Educator

The given relation ` tan lambda = (cos phi_n*tan lambda- mu)/(cos phi_n + mu*tan lambda) ` cannot be proved.

As seen from the link provided in the question the back drive efficiency is given by `e_b = (1/tan lambda)*(cos phi_n*tan lambda- mu)/(cos phi_n + mu*tan lambda)` where `mu` is the coefficient of friction. As all the values in the expression are dimensionless, the back drive efficiency is also a dimensionless scalar. This does not mean that `tan lambda = (cos phi_n*tan lambda- mu)/(cos phi_n + mu*tan lambda)`. All the values on the right are scalars that when multiplied, subtracted, added and divided together give a scalar that is the value on the left.

alfimulia | Student

the equation 10 and 11 is derived from one equation Torque drive.

how to trace back equation 10 and 11, to their origin formula

revert back to their ancestor ?