Where Ncr is the critical speed and f is the bending
frequency. Considering that the natural frequency
of a shaft according to the above equation is
inversely proportional to the square of shaft's
length and is proportional to the square root of
Young's modulus, the conventional steel drive
shafts are made of two pieces to increase the
natural frequency of the shaft, which results in
overall increase in the weight of the shaft. So, in
order to increase the natural frequency, the length
of shaft should be reduced or E / ratio should
be increased. Despite the space limitations that
confines outer shaft diameter , the only way to
increase the critical speed is to increase
E / ratio (specific modulus)