Concentricity is a measure of "roundness" either between two objects of similar diameters (but slightly different OD/ID ratio of wall thickness along the centerline of the objects) or for shafts, it is a measure of outer diameter variation as measured along the true centerline of the shaft.
For example, a shaft journal that is round about it's centerline is considered a concentric diameter about the bearing. A second example pertains to the comparison of two separate pipe spools that need to be butt welded. One pipe section may have a slight variation in wall thickness ratio that results in one side of the pipe section touching and opposite there is a gap if the two pipe spools are aligned along their longitudinal axis. This would be an example of non-concentric diameters.
The TIR refers to a measure of the total indicated runout for a shaft about a selected centerline. Typically, a zero point is arbitrally chosen with a dial indicator. As the shaft is rotated, the runout is measured starting from 0. The maximum dial indicator reading is recorded as the TIR for that point along the shaft axis. Typically, numerous readings are obtained along the length of the shaft to determine TIR.
Now, there is no direct correlation between TIR and concentricity because depending on the centerline that is used, you can get a different measure of concentricity and TIR. Normally, TIR is obtained by placing the shaft in a lathe between machined centers. However, if the centers are off or a different method of support is used for the shaft, the concentricity of the shaft will not be measured with respect to the true centerline of the shaft.
For example, lets suppose you have a shaft that sustained damage to a journal. The shaft cannot be removed from the machine so you are forced to obtain TIR and concentricity readings between the journal and bearing. The TIR can be measured from any reference point along the shaft provided you remain consistent when measuring TIR with the dial indicator. Here you are measuring shaft deflection as the shaft is rotated.
To measure concentricity of the shaft journal you need to know the original location of the shaft centerline. If the shaft has moved from its original centerline, the diameters can be determined with micrometers but will not be a true measure of concentricity between the journal and bearing.
