# Equation describing the contraction of a rotation shaft

by Christopher99
Tags: generators, rotational dynamics, shaft, turbines
 P: 3 It's a fact that a shaft in a turbine is expanding when the temperature is increasing. A simple equation gives that the expansion can be described as: deltaX=(T1-T0)*alpha*x0, where deltaX is the expansion, T0 is the initial temperature, T1 is the final temperature and alpha is a coefficient (approximately equal to 11.5*10^-6 /°C). At least this fomula is accurate when the temperature is in the range 0- 100 °C. However, how can the contraction (in length) due to rotation be calculated? Until very recently I was not even aware that this was something that could be measured if we for instance is talking about a shaft that is 25 m long and 0.6 m i diameter rotating in 3000 rpm. I've been told that this effect is the same as the temperature expansion which means the length of the shaft is not changed at all when the turbine is running on full power if it's designed correctly. Any ideas?
 Sci Advisor P: 5,095 It's going to depend on how the shaft is constrained within the turbine, i.e. bearing and lock nut locations (if used). Without looking over the shaft layout it's impossible to say. You have a lot of things other than centrifugals to worry about. If all else fails, use conservation of mass. Use the standard shaft dimensions to calculate a volume. Then use the new OD and ID with the volume you just calculated to calculate a new length. Again, this assumes that the shaft is completely unconstrained and is allowed to move over its entire length.
P: 3
 Quote by FredGarvin It's going to depend on how the shaft is constrained within the turbine, i.e. bearing and lock nut locations (if used). Without looking over the shaft layout it's impossible to say. You have a lot of things other than centrifugals to worry about. If all else fails, use conservation of mass. Use the standard shaft dimensions to calculate a volume. Then use the new OD and ID with the volume you just calculated to calculate a new length. Again, this assumes that the shaft is completely unconstrained and is allowed to move over its entire length.