An enclosed fan-cooled induction motor has a thermal time constant of τθ=3 h and a steady-state rated temperature of θf=120 °C at an ambient temperature of θamb=40 °C. The motor has at time t=0_a temperature of θ=θamb, and the motor is fully loaded at t=0+. Calculate the time t95% when the fully loaded motor reaches 95% of its final temperature θf=120 °C.
With Eq. 6-39 one obtains
θ=θf−(θf−θo)⋅e(−t/τθ) (6-39)
or t95%=2.59⋅τθ=7.77 h.